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-   -   find very easy twin prime in the infamy twin primes (https://www.mersenneforum.org/showthread.php?t=23617)

 hal1se 2018-08-29 18:26

find very easy twin prime in the infamy twin primes

every prime templates probably twin prime, all template elements very regularly!

3# template probably twin or cousin prime=1
5# template probably twin or cousin prime=3
7# template probably twin or cousin prime=15=3*5
11# tepmlate probably twin or cousin prime=135=3^3*5
13# template probably twin or cousin prime=1485=3^3*5*11
17# template probably twin or cousin prime=22275=3^4*5^2*11
19# template probably twin or cousin prime=378675=3^4*5^2*11*17
23# template probably twin or cousin prime=7952175=3^5*5^2*7*11*17

some one see, any regularly?
you must: look hyper geometric and complex variables domain!
________________
if we think, only prime template last probably element:
________________

3# to 5# twimprime count, only (6n+5, 6n+6+1) format = 2
(11, 13)
(17, 19)
3#=2*3 to 5#=2*3*5 range
2*3*5 - 2*3 = 2*3*(5-1)=3#*(5-1)
3#*(5-1)/6=(5-1) =4
(3#*n+3#-1, 3#*n+3#+1) format numbers

5# to 7# twinprime count, only (30n+29, 30n+30+1) format = 3
(59, 61)
(149, 151)
(179, 181)
5#=2*3*5 to 7#=2*3*5*7 range
2*3*5*7 - 2*3*5 = 2*3*5*(7-1)=5#*(7-1)
5#*(7-1)/5#=(7-1) =6 times :(5#*n+5#-1, 5#*n+5#+1) format numbers

3# to 5#
1*isprime(3#*1+(3#-1))*isprime(3#*1+(3#+1))
2*isprime(3#*2+(3#-1))*isprime(3#*2+(3#+1))
3*isprime(3#*3+(3#-1))*isprime(3#*3+(3#+1))
4*isprime(3#*4+(3#-1))*isprime(3#*4+(3#+1))
4: probably template last twin elements
n=1,2,4 : 3 twinprimes
__
5# to 7#
1*isprime(5#*1+(5#-1))*isprime(5#*1+(5#+1))
2*isprime(5#*2+(5#-1))*isprime(5#*2+(5#+1))
3*isprime(5#*3+(5#-1))*isprime(5#*3+(5#+1))
4*isprime(5#*4+(5#-1))*isprime(5#*4+(5#+1))
5*isprime(5#*5+(5#-1))*isprime(5#*5+(5#+1))
6*isprime(5#*6+(5#-1))*isprime(5#*6+(5#+1))
n=1,4,5 : 3 twinprimes
__
7# to 11#
1*isprime(7#*1+(7#-1))*isprime(7#*1+(7#+1))
2*isprime(7#*2+(7#-1))*isprime(7#*2+(7#+1))
3*isprime(7#*3+(7#-1))*isprime(7#*3+(7#+1))
4*isprime(7#*4+(7#-1))*isprime(7#*4+(7#+1))
5*isprime(7#*5+(7#-1))*isprime(7#*5+(7#+1))
6*isprime(7#*6+(7#-1))*isprime(7#*6+(7#+1))
7*isprime(7#*7+(7#-1))*isprime(7#*7+(7#+1))
8*isprime(7#*8+(7#-1))*isprime(7#*8+(7#+1))
9*isprime(7#*9+(7#-1))*isprime(7#*9+(7#+1))
10*isprime(7#*10+(7#-1))*isprime(7#*10+(7#+1))
n=1,4,10 : 3 twinprimes
__
11# to 13#
1*isprime(11#*1+(11#-1))*isprime(11#*1+(11#+1))
2*isprime(11#*2+(11#-1))*isprime(11#*2+(11#+1))
3*isprime(11#*3+(11#-1))*isprime(11#*3+(11#+1))
4*isprime(11#*4+(11#-1))*isprime(11#*4+(11#+1))
5*isprime(11#*5+(11#-1))*isprime(11#*5+(11#+1))
6*isprime(11#*6+(11#-1))*isprime(11#*6+(11#+1))
7*isprime(11#*7+(11#-1))*isprime(11#*7+(11#+1))
8*isprime(11#*8+(11#-1))*isprime(11#*8+(11#+1))
9*isprime(11#*9+(11#-1))*isprime(11#*9+(11#+1))
10*isprime(11#*10+(11#-1))*isprime(11#*10+(11#+1))
11*isprime(11#*11+(11#-1))*isprime(11#*11+(11#+1))
12*isprime(11#*12+(11#-1))*isprime(11#*12+(11#+1))
n=3,4,10 : 3 twinprimes
__
13# to 17#
1*isprime(13#*1+(13#-1))*isprime(13#*1+(13#+1))
2*isprime(13#*2+(13#-1))*isprime(13#*2+(13#+1))
3*isprime(13#*3+(13#-1))*isprime(13#*3+(13#+1))
4*isprime(13#*4+(13#-1))*isprime(13#*4+(13#+1))
5*isprime(13#*5+(13#-1))*isprime(13#*5+(13#+1))
6*isprime(13#*6+(13#-1))*isprime(13#*6+(13#+1))
7*isprime(13#*7+(13#-1))*isprime(13#*7+(13#+1))
8*isprime(13#*8+(13#-1))*isprime(13#*8+(13#+1))
9*isprime(13#*9+(13#-1))*isprime(13#*9+(13#+1))
10*isprime(13#*10+(13#-1))*isprime(13#*10+(13#+1))
11*isprime(13#*11+(13#-1))*isprime(13#*11+(13#+1))
12*isprime(13#*12+(13#-1))*isprime(13#*12+(13#+1))
13*isprime(13#*13+(13#-1))*isprime(13#*13+(13#+1))
14*isprime(13#*14+(13#-1))*isprime(13#*14+(13#+1))
15*isprime(13#*15+(13#-1))*isprime(13#*15+(13#+1))
16*isprime(13#*16+(13#-1))*isprime(13#*16+(13#+1))
n=5,8,9,10,12,13 : 6 twinprimes

__
17# to 19#
1*isprime(17#*1+(17#-1))*isprime(17#*1+(17#+1))
2*isprime(17#*2+(17#-1))*isprime(17#*2+(17#+1))
3*isprime(17#*3+(17#-1))*isprime(17#*3+(17#+1))
4*isprime(17#*4+(17#-1))*isprime(17#*4+(17#+1))
5*isprime(17#*5+(17#-1))*isprime(17#*5+(17#+1))
6*isprime(17#*6+(17#-1))*isprime(17#*6+(17#+1))
7*isprime(17#*7+(17#-1))*isprime(17#*7+(17#+1))
8*isprime(17#*8+(17#-1))*isprime(17#*8+(17#+1))
9*isprime(17#*9+(17#-1))*isprime(17#*9+(17#+1))
10*isprime(17#*10+(17#-1))*isprime(17#*10+(17#+1))
11*isprime(17#*11+(17#-1))*isprime(17#*11+(17#+1))
12*isprime(17#*12+(17#-1))*isprime(17#*12+(17#+1))
13*isprime(17#*13+(17#-1))*isprime(17#*13+(17#+1))
14*isprime(17#*14+(17#-1))*isprime(17#*14+(17#+1))
15*isprime(17#*15+(17#-1))*isprime(17#*15+(17#+1))
16*isprime(17#*16+(17#-1))*isprime(17#*16+(17#+1))
17*isprime(17#*17+(17#-1))*isprime(17#*17+(17#+1))
18*isprime(17#*18+(17#-1))*isprime(17#*18+(17#+1))
n=7,16 : 2 twin primes

__
19# to 23#
1*isprime(19#*1+(19#-1))*isprime(19#*1+(19#+1))
2*isprime(19#*2+(19#-1))*isprime(19#*2+(19#+1))
3*isprime(19#*3+(19#-1))*isprime(19#*3+(19#+1))
4*isprime(19#*4+(19#-1))*isprime(19#*4+(19#+1))
5*isprime(19#*5+(19#-1))*isprime(19#*5+(19#+1))
6*isprime(19#*6+(19#-1))*isprime(19#*6+(19#+1))
7*isprime(19#*7+(19#-1))*isprime(19#*7+(19#+1))
8*isprime(19#*8+(19#-1))*isprime(19#*8+(19#+1))
9*isprime(19#*9+(19#-1))*isprime(19#*9+(19#+1))
10*isprime(19#*10+(19#-1))*isprime(19#*10+(19#+1))
11*isprime(19#*11+(19#-1))*isprime(19#*11+(19#+1))
12*isprime(19#*12+(19#-1))*isprime(19#*12+(19#+1))
13*isprime(19#*13+(19#-1))*isprime(19#*13+(19#+1))
14*isprime(19#*14+(19#-1))*isprime(19#*14+(19#+1))
15*isprime(19#*15+(19#-1))*isprime(19#*15+(19#+1))
16*isprime(19#*16+(19#-1))*isprime(19#*16+(19#+1))
17*isprime(19#*17+(19#-1))*isprime(19#*17+(19#+1))
18*isprime(19#*18+(19#-1))*isprime(19#*18+(19#+1))
19*isprime(19#*19+(19#-1))*isprime(19#*19+(19#+1))
20*isprime(19#*20+(19#-1))*isprime(19#*20+(19#+1))
21*isprime(19#*21+(19#-1))*isprime(19#*21+(19#+1))
22*isprime(19#*22+(19#-1))*isprime(19#*22+(19#+1))
n=10 : only 1 twinprime
__

23# to 29#
1*isprime(23#*1+(23#-1))*isprime(23#*1+(23#+1))
2*isprime(23#*2+(23#-1))*isprime(23#*2+(23#+1))
3*isprime(23#*3+(23#-1))*isprime(23#*3+(23#+1))
4*isprime(23#*4+(23#-1))*isprime(23#*4+(23#+1))
5*isprime(23#*5+(23#-1))*isprime(23#*5+(23#+1))
6*isprime(23#*6+(23#-1))*isprime(23#*6+(23#+1))
7*isprime(23#*7+(23#-1))*isprime(23#*7+(23#+1))
8*isprime(23#*8+(23#-1))*isprime(23#*8+(23#+1))
9*isprime(23#*9+(23#-1))*isprime(23#*9+(23#+1))
10*isprime(23#*10+(23#-1))*isprime(23#*10+(23#+1))
11*isprime(23#*11+(23#-1))*isprime(23#*11+(23#+1))
12*isprime(23#*12+(23#-1))*isprime(23#*12+(23#+1))
13*isprime(23#*13+(23#-1))*isprime(23#*13+(23#+1))
14*isprime(23#*14+(23#-1))*isprime(23#*14+(23#+1))
15*isprime(23#*15+(23#-1))*isprime(23#*15+(23#+1))
16*isprime(23#*16+(23#-1))*isprime(23#*16+(23#+1))
17*isprime(23#*17+(23#-1))*isprime(23#*17+(23#+1))
18*isprime(23#*18+(23#-1))*isprime(23#*18+(23#+1))
19*isprime(23#*19+(23#-1))*isprime(23#*19+(23#+1))
20*isprime(23#*20+(23#-1))*isprime(23#*20+(23#+1))
21*isprime(23#*21+(23#-1))*isprime(23#*21+(23#+1))
22*isprime(23#*22+(23#-1))*isprime(23#*22+(23#+1))
23*isprime(23#*23+(23#-1))*isprime(23#*23+(23#+1))
24*isprime(23#*24+(23#-1))*isprime(23#*24+(23#+1))
25*isprime(23#*25+(23#-1))*isprime(23#*25+(23#+1))
26*isprime(23#*26+(23#-1))*isprime(23#*26+(23#+1))
27*isprime(23#*27+(23#-1))*isprime(23#*27+(23#+1))
28*isprime(23#*28+(23#-1))*isprime(23#*28+(23#+1))
n=3,10,15,18,19,21,26: 7 twinprime

__
29# to 31#
15*isprime(29#*15+(29#-1))*isprime(29#*15+(29#+1))
only 1 twin prime

___
31# to 37#
21*isprime(31#*21+(31#-1))*isprime(31#*21+(31#+1))
only 1 twin prime

__
37# to 41#
3*isprime(37#*3+(37#-1))*isprime(37#*3+(37#+1))
22*isprime(37#*22+(37#-1))*isprime(37#*22+(37#+1))

middle point of range:
37#*(41+1)/2=155835500831010
ln(155835500831010)=32,679822084968449905680465344453
every (3/4)*(32,679822084968449905680465344453)^2=
=800,978=~801 integers only 1 twin prime, average, this range.
40 probably template last element twinprime!
but 2 twin prime!
range twin prime last element count posibilities > normal distribition posibilites!

__
41# to 43#
no twin prime!
very normal and near normal distribition posibilites result!

__
43# to 47#
23*isprime(43#*23+(43#-1))*isprime(43#*23+(43#+1))
only 1 twin prime

__
47# to 53#
36*isprime(47#*36+(47#-1))*isprime(47#*36+(47#+1))
(22750921955774182169,22750921955774182171)
only 1 twin prime.

__
53# to 59#
1*isprime(53#*1+(53#-1))*isprime(53#*1+(53#+1))
2*isprime(53#*2+(53#-1))*isprime(53#*2+(53#+1))
3*isprime(53#*3+(53#-1))*isprime(53#*3+(53#+1))
4*isprime(53#*4+(53#-1))*isprime(53#*4+(53#+1))
5*isprime(53#*5+(53#-1))*isprime(53#*5+(53#+1))
6*isprime(53#*6+(53#-1))*isprime(53#*6+(53#+1))
7*isprime(53#*7+(53#-1))*isprime(53#*7+(53#+1))
8*isprime(53#*8+(53#-1))*isprime(53#*8+(53#+1))
9*isprime(53#*9+(53#-1))*isprime(53#*9+(53#+1))
10*isprime(53#*10+(53#-1))*isprime(53#*10+(53#+1))
11*isprime(53#*11+(53#-1))*isprime(53#*11+(53#+1))
12*isprime(53#*12+(53#-1))*isprime(53#*12+(53#+1))
13*isprime(53#*13+(53#-1))*isprime(53#*13+(53#+1))
14*isprime(53#*14+(53#-1))*isprime(53#*14+(53#+1))
15*isprime(53#*15+(53#-1))*isprime(53#*15+(53#+1))
16*isprime(53#*16+(53#-1))*isprime(53#*16+(53#+1))
17*isprime(53#*17+(53#-1))*isprime(53#*17+(53#+1))
18*isprime(53#*18+(53#-1))*isprime(53#*18+(53#+1))
19*isprime(53#*19+(53#-1))*isprime(53#*19+(53#+1))
20*isprime(53#*20+(53#-1))*isprime(53#*20+(53#+1))
21*isprime(53#*21+(53#-1))*isprime(53#*21+(53#+1))
22*isprime(53#*22+(53#-1))*isprime(53#*22+(53#+1))
23*isprime(53#*23+(53#-1))*isprime(53#*23+(53#+1))
24*isprime(53#*24+(53#-1))*isprime(53#*24+(53#+1))
25*isprime(53#*25+(53#-1))*isprime(53#*25+(53#+1))
26*isprime(53#*26+(53#-1))*isprime(53#*26+(53#+1))
27*isprime(53#*27+(53#-1))*isprime(53#*27+(53#+1))
28*isprime(53#*28+(53#-1))*isprime(53#*28+(53#+1))
29*isprime(53#*29+(53#-1))*isprime(53#*29+(53#+1))
30*isprime(53#*30+(53#-1))*isprime(53#*30+(53#+1))
31*isprime(53#*31+(53#-1))*isprime(53#*31+(53#+1))
32*isprime(53#*32+(53#-1))*isprime(53#*32+(53#+1))
33*isprime(53#*33+(53#-1))*isprime(53#*33+(53#+1))
34*isprime(53#*34+(53#-1))*isprime(53#*34+(53#+1))
35*isprime(53#*35+(53#-1))*isprime(53#*35+(53#+1))
36*isprime(53#*36+(53#-1))*isprime(53#*36+(53#+1))
37*isprime(53#*37+(53#-1))*isprime(53#*37+(53#+1))
38*isprime(53#*38+(53#-1))*isprime(53#*38+(53#+1))
39*isprime(53#*39+(53#-1))*isprime(53#*39+(53#+1))
40*isprime(53#*40+(53#-1))*isprime(53#*40+(53#+1))
41*isprime(53#*41+(53#-1))*isprime(53#*41+(53#+1))
42*isprime(53#*42+(53#-1))*isprime(53#*42+(53#+1))
43*isprime(53#*43+(53#-1))*isprime(53#*43+(53#+1))
44*isprime(53#*44+(53#-1))*isprime(53#*44+(53#+1))
45*isprime(53#*45+(53#-1))*isprime(53#*45+(53#+1))
46*isprime(53#*46+(53#-1))*isprime(53#*46+(53#+1))
47*isprime(53#*47+(53#-1))*isprime(53#*47+(53#+1))
48*isprime(53#*48+(53#-1))*isprime(53#*48+(53#+1))
49*isprime(53#*49+(53#-1))*isprime(53#*49+(53#+1))
50*isprime(53#*50+(53#-1))*isprime(53#*50+(53#+1))
51*isprime(53#*51+(53#-1))*isprime(53#*51+(53#+1))
52*isprime(53#*52+(53#-1))*isprime(53#*52+(53#+1))
53*isprime(53#*53+(53#-1))*isprime(53#*53+(53#+1))
54*isprime(53#*54+(53#-1))*isprime(53#*54+(53#+1))
55*isprime(53#*55+(53#-1))*isprime(53#*55+(53#+1))
56*isprime(53#*56+(53#-1))*isprime(53#*56+(53#+1))
57*isprime(53#*57+(53#-1))*isprime(53#*57+(53#+1))
58*isprime(53#*58+(53#-1))*isprime(53#*58+(53#+1))
n=27: only 1 twin prime!
912496437361321252439
912496437361321252441

range 53# to 59#
probably tepmlate last element:58
middle point of range:
(53#+59#)/2=53# *(1+59)/2=53# *30=977674754315701341900
range average twin prime rate:
(3/4)*(ln(977674754315701341900))^2=1751,96555=~1752
every 1752 numbers average 1 twin prime in the range:53# to 59#

but probably 58 twin prime test: how do not see we, posible 0 twinprime, surprise: 1 twin prime!
how is it, posibilities > normal distribition posibilities?

note: i am an autistic,alzheimer, parcinson, etc.., brain damage.
please do not see, my fault!
important question: how is it, temlate last element twin prime posibilities > normal distribition posibilities?
__
range 59# to 61#
template 59#: last probably prime elements: only = 60.
10*isprime(61#*10+(61#-1))*isprime(61#*10+(61#+1))
n=10
1290172194953476680815969
1290172194953476680815971
1 twin prime surprise!
normal posibilities: 0 twin prime count highly reality!
1 twin prime count posibilities very low posibilities!
but how is it, 1 twin prime count?

__
range 61# to 67#
range 117288381359406970983270 to 7858321551080267055879090
24 decimal digit to 25 decimal digit.
10*isprime(61#*10+(61#-1))*isprime(61#*10+(61#+1))
n=10: 1 twin prime!
1290172194953476680815969
1290172194953476680815969+2

only 66 probably twin prime test: but 25 decimal digits twinprime easy!
how is it, posibilities > normal distribition posibilities?

__
range: 67# to 71#
1*isprime(67#*1+(67#-1))*isprime(67#*1+(67#+1))
2*isprime(67#*2+(67#-1))*isprime(67#*2+(67#+1))
3*isprime(67#*3+(67#-1))*isprime(67#*3+(67#+1))
4*isprime(67#*4+(67#-1))*isprime(67#*4+(67#+1))
5*isprime(67#*5+(67#-1))*isprime(67#*5+(67#+1))
6*isprime(67#*6+(67#-1))*isprime(67#*6+(67#+1))
7*isprime(67#*7+(67#-1))*isprime(67#*7+(67#+1))
8*isprime(67#*8+(67#-1))*isprime(67#*8+(67#+1))
9*isprime(67#*9+(67#-1))*isprime(67#*9+(67#+1))
10*isprime(67#*10+(67#-1))*isprime(67#*10+(67#+1))
11*isprime(67#*11+(67#-1))*isprime(67#*11+(67#+1))
12*isprime(67#*12+(67#-1))*isprime(67#*12+(67#+1))
13*isprime(67#*13+(67#-1))*isprime(67#*13+(67#+1))
14*isprime(67#*14+(67#-1))*isprime(67#*14+(67#+1))
15*isprime(67#*15+(67#-1))*isprime(67#*15+(67#+1))
16*isprime(67#*16+(67#-1))*isprime(67#*16+(67#+1))
17*isprime(67#*17+(67#-1))*isprime(67#*17+(67#+1))
18*isprime(67#*18+(67#-1))*isprime(67#*18+(67#+1))
19*isprime(67#*19+(67#-1))*isprime(67#*19+(67#+1))
20*isprime(67#*20+(67#-1))*isprime(67#*20+(67#+1))
21*isprime(67#*21+(67#-1))*isprime(67#*21+(67#+1))
22*isprime(67#*22+(67#-1))*isprime(67#*22+(67#+1))
23*isprime(67#*23+(67#-1))*isprime(67#*23+(67#+1))
24*isprime(67#*24+(67#-1))*isprime(67#*24+(67#+1))
25*isprime(67#*25+(67#-1))*isprime(67#*25+(67#+1))
26*isprime(67#*26+(67#-1))*isprime(67#*26+(67#+1))
27*isprime(67#*27+(67#-1))*isprime(67#*27+(67#+1))
28*isprime(67#*28+(67#-1))*isprime(67#*28+(67#+1))
29*isprime(67#*29+(67#-1))*isprime(67#*29+(67#+1))
30*isprime(67#*30+(67#-1))*isprime(67#*30+(67#+1))
31*isprime(67#*31+(67#-1))*isprime(67#*31+(67#+1))
32*isprime(67#*32+(67#-1))*isprime(67#*32+(67#+1))
33*isprime(67#*33+(67#-1))*isprime(67#*33+(67#+1))
34*isprime(67#*34+(67#-1))*isprime(67#*34+(67#+1))
35*isprime(67#*35+(67#-1))*isprime(67#*35+(67#+1))
36*isprime(67#*36+(67#-1))*isprime(67#*36+(67#+1))
37*isprime(67#*37+(67#-1))*isprime(67#*37+(67#+1))
38*isprime(67#*38+(67#-1))*isprime(67#*38+(67#+1))
39*isprime(67#*39+(67#-1))*isprime(67#*39+(67#+1))
40*isprime(67#*40+(67#-1))*isprime(67#*40+(67#+1))
41*isprime(67#*41+(67#-1))*isprime(67#*41+(67#+1))
42*isprime(67#*42+(67#-1))*isprime(67#*42+(67#+1))
43*isprime(67#*43+(67#-1))*isprime(67#*43+(67#+1))
44*isprime(67#*44+(67#-1))*isprime(67#*44+(67#+1))
45*isprime(67#*45+(67#-1))*isprime(67#*45+(67#+1))
46*isprime(67#*46+(67#-1))*isprime(67#*46+(67#+1))
47*isprime(67#*47+(67#-1))*isprime(67#*47+(67#+1))
48*isprime(67#*48+(67#-1))*isprime(67#*48+(67#+1))
49*isprime(67#*49+(67#-1))*isprime(67#*49+(67#+1))
50*isprime(67#*50+(67#-1))*isprime(67#*50+(67#+1))
51*isprime(67#*51+(67#-1))*isprime(67#*51+(67#+1))
52*isprime(67#*52+(67#-1))*isprime(67#*52+(67#+1))
53*isprime(67#*53+(67#-1))*isprime(67#*53+(67#+1))
54*isprime(67#*54+(67#-1))*isprime(67#*54+(67#+1))
55*isprime(67#*55+(67#-1))*isprime(67#*55+(67#+1))
56*isprime(67#*56+(67#-1))*isprime(67#*56+(67#+1))
57*isprime(67#*57+(67#-1))*isprime(67#*57+(67#+1))
58*isprime(67#*58+(67#-1))*isprime(67#*58+(67#+1))
59*isprime(67#*59+(67#-1))*isprime(67#*59+(67#+1))
60*isprime(67#*60+(67#-1))*isprime(67#*60+(67#+1))
61*isprime(67#*61+(67#-1))*isprime(67#*61+(67#+1))
62*isprime(67#*62+(67#-1))*isprime(67#*62+(67#+1))
63*isprime(67#*63+(67#-1))*isprime(67#*63+(67#+1))
64*isprime(67#*64+(67#-1))*isprime(67#*64+(67#+1))
65*isprime(67#*65+(67#-1))*isprime(67#*65+(67#+1))
66*isprime(67#*66+(67#-1))*isprime(67#*66+(67#+1))
67*isprime(67#*67+(67#-1))*isprime(67#*67+(67#+1))
68*isprime(67#*68+(67#-1))*isprime(67#*68+(67#+1))
69*isprime(67#*69+(67#-1))*isprime(67#*69+(67#+1))
70*isprime(67#*70+(67#-1))*isprime(67#*70+(67#+1))

0 twin prime in 70 probably twin primes.
very normal result!

__
range: 71# to 73#
1*isprime(71#*1+(71#-1))*isprime(71#*1+(71#+1))
2*isprime(71#*2+(71#-1))*isprime(71#*2+(71#+1))
3*isprime(71#*3+(71#-1))*isprime(71#*3+(71#+1))
4*isprime(71#*4+(71#-1))*isprime(71#*4+(71#+1))
5*isprime(71#*5+(71#-1))*isprime(71#*5+(71#+1))
6*isprime(71#*6+(71#-1))*isprime(71#*6+(71#+1))
7*isprime(71#*7+(71#-1))*isprime(71#*7+(71#+1))
8*isprime(71#*8+(71#-1))*isprime(71#*8+(71#+1))
9*isprime(71#*9+(71#-1))*isprime(71#*9+(71#+1))
10*isprime(71#*10+(71#-1))*isprime(71#*10+(71#+1))
11*isprime(71#*11+(71#-1))*isprime(71#*11+(71#+1))
12*isprime(71#*12+(71#-1))*isprime(71#*12+(71#+1))
13*isprime(71#*13+(71#-1))*isprime(71#*13+(71#+1))
14*isprime(71#*14+(71#-1))*isprime(71#*14+(71#+1))
15*isprime(71#*15+(71#-1))*isprime(71#*15+(71#+1))
16*isprime(71#*16+(71#-1))*isprime(71#*16+(71#+1))
17*isprime(71#*17+(71#-1))*isprime(71#*17+(71#+1))
18*isprime(71#*18+(71#-1))*isprime(71#*18+(71#+1))
19*isprime(71#*19+(71#-1))*isprime(71#*19+(71#+1))
20*isprime(71#*20+(71#-1))*isprime(71#*20+(71#+1))
21*isprime(71#*21+(71#-1))*isprime(71#*21+(71#+1))
22*isprime(71#*22+(71#-1))*isprime(71#*22+(71#+1))
23*isprime(71#*23+(71#-1))*isprime(71#*23+(71#+1))
24*isprime(71#*24+(71#-1))*isprime(71#*24+(71#+1))
25*isprime(71#*25+(71#-1))*isprime(71#*25+(71#+1))
26*isprime(71#*26+(71#-1))*isprime(71#*26+(71#+1))
27*isprime(71#*27+(71#-1))*isprime(71#*27+(71#+1))
28*isprime(71#*28+(71#-1))*isprime(71#*28+(71#+1))
29*isprime(71#*29+(71#-1))*isprime(71#*29+(71#+1))
30*isprime(71#*30+(71#-1))*isprime(71#*30+(71#+1))
31*isprime(71#*31+(71#-1))*isprime(71#*31+(71#+1))
32*isprime(71#*32+(71#-1))*isprime(71#*32+(71#+1))
33*isprime(71#*33+(71#-1))*isprime(71#*33+(71#+1))
34*isprime(71#*34+(71#-1))*isprime(71#*34+(71#+1))
35*isprime(71#*35+(71#-1))*isprime(71#*35+(71#+1))
36*isprime(71#*36+(71#-1))*isprime(71#*36+(71#+1))
37*isprime(71#*37+(71#-1))*isprime(71#*37+(71#+1))
38*isprime(71#*38+(71#-1))*isprime(71#*38+(71#+1))
39*isprime(71#*39+(71#-1))*isprime(71#*39+(71#+1))
40*isprime(71#*40+(71#-1))*isprime(71#*40+(71#+1))
41*isprime(71#*41+(71#-1))*isprime(71#*41+(71#+1))
42*isprime(71#*42+(71#-1))*isprime(71#*42+(71#+1))
43*isprime(71#*43+(71#-1))*isprime(71#*43+(71#+1))
44*isprime(71#*44+(71#-1))*isprime(71#*44+(71#+1))
45*isprime(71#*45+(71#-1))*isprime(71#*45+(71#+1))
46*isprime(71#*46+(71#-1))*isprime(71#*46+(71#+1))
47*isprime(71#*47+(71#-1))*isprime(71#*47+(71#+1))
48*isprime(71#*48+(71#-1))*isprime(71#*48+(71#+1))
49*isprime(71#*49+(71#-1))*isprime(71#*49+(71#+1))
50*isprime(71#*50+(71#-1))*isprime(71#*50+(71#+1))
51*isprime(71#*51+(71#-1))*isprime(71#*51+(71#+1))
52*isprime(71#*52+(71#-1))*isprime(71#*52+(71#+1))
53*isprime(71#*53+(71#-1))*isprime(71#*53+(71#+1))
54*isprime(71#*54+(71#-1))*isprime(71#*54+(71#+1))
55*isprime(71#*55+(71#-1))*isprime(71#*55+(71#+1))
56*isprime(71#*56+(71#-1))*isprime(71#*56+(71#+1))
57*isprime(71#*57+(71#-1))*isprime(71#*57+(71#+1))
58*isprime(71#*58+(71#-1))*isprime(71#*58+(71#+1))
59*isprime(71#*59+(71#-1))*isprime(71#*59+(71#+1))
60*isprime(71#*60+(71#-1))*isprime(71#*60+(71#+1))
61*isprime(71#*61+(71#-1))*isprime(71#*61+(71#+1))
62*isprime(71#*62+(71#-1))*isprime(71#*62+(71#+1))
63*isprime(71#*63+(71#-1))*isprime(71#*63+(71#+1))
64*isprime(71#*64+(71#-1))*isprime(71#*64+(71#+1))
65*isprime(71#*65+(71#-1))*isprime(71#*65+(71#+1))
66*isprime(71#*66+(71#-1))*isprime(71#*66+(71#+1))
67*isprime(71#*67+(71#-1))*isprime(71#*67+(71#+1))
68*isprime(71#*68+(71#-1))*isprime(71#*68+(71#+1))
69*isprime(71#*69+(71#-1))*isprime(71#*69+(71#+1))
70*isprime(71#*70+(71#-1))*isprime(71#*70+(71#+1))
71*isprime(71#*71+(71#-1))*isprime(71#*71+(71#+1))
72*isprime(71#*72+(71#-1))*isprime(71#*72+(71#+1))

n=10,14,52,63

very much twin prime in the probably 72 twin primes!
__
range: 73# to 79#
1*isprime(73#*1+(73#-1))*isprime(73#*1+(73#+1))
2*isprime(73#*2+(73#-1))*isprime(73#*2+(73#+1))
3*isprime(73#*3+(73#-1))*isprime(73#*3+(73#+1))
4*isprime(73#*4+(73#-1))*isprime(73#*4+(73#+1))
5*isprime(73#*5+(73#-1))*isprime(73#*5+(73#+1))
6*isprime(73#*6+(73#-1))*isprime(73#*6+(73#+1))
7*isprime(73#*7+(73#-1))*isprime(73#*7+(73#+1))
8*isprime(73#*8+(73#-1))*isprime(73#*8+(73#+1))
9*isprime(73#*9+(73#-1))*isprime(73#*9+(73#+1))
10*isprime(73#*10+(73#-1))*isprime(73#*10+(73#+1))
11*isprime(73#*11+(73#-1))*isprime(73#*11+(73#+1))
12*isprime(73#*12+(73#-1))*isprime(73#*12+(73#+1))
13*isprime(73#*13+(73#-1))*isprime(73#*13+(73#+1))
14*isprime(73#*14+(73#-1))*isprime(73#*14+(73#+1))
15*isprime(73#*15+(73#-1))*isprime(73#*15+(73#+1))
16*isprime(73#*16+(73#-1))*isprime(73#*16+(73#+1))
17*isprime(73#*17+(73#-1))*isprime(73#*17+(73#+1))
18*isprime(73#*18+(73#-1))*isprime(73#*18+(73#+1))
19*isprime(73#*19+(73#-1))*isprime(73#*19+(73#+1))
20*isprime(73#*20+(73#-1))*isprime(73#*20+(73#+1))
21*isprime(73#*21+(73#-1))*isprime(73#*21+(73#+1))
22*isprime(73#*22+(73#-1))*isprime(73#*22+(73#+1))
23*isprime(73#*23+(73#-1))*isprime(73#*23+(73#+1))
24*isprime(73#*24+(73#-1))*isprime(73#*24+(73#+1))
25*isprime(73#*25+(73#-1))*isprime(73#*25+(73#+1))
26*isprime(73#*26+(73#-1))*isprime(73#*26+(73#+1))
27*isprime(73#*27+(73#-1))*isprime(73#*27+(73#+1))
28*isprime(73#*28+(73#-1))*isprime(73#*28+(73#+1))
29*isprime(73#*29+(73#-1))*isprime(73#*29+(73#+1))
30*isprime(73#*30+(73#-1))*isprime(73#*30+(73#+1))
31*isprime(73#*31+(73#-1))*isprime(73#*31+(73#+1))
32*isprime(73#*32+(73#-1))*isprime(73#*32+(73#+1))
33*isprime(73#*33+(73#-1))*isprime(73#*33+(73#+1))
34*isprime(73#*34+(73#-1))*isprime(73#*34+(73#+1))
35*isprime(73#*35+(73#-1))*isprime(73#*35+(73#+1))
36*isprime(73#*36+(73#-1))*isprime(73#*36+(73#+1))
37*isprime(73#*37+(73#-1))*isprime(73#*37+(73#+1))
38*isprime(73#*38+(73#-1))*isprime(73#*38+(73#+1))
39*isprime(73#*39+(73#-1))*isprime(73#*39+(73#+1))
40*isprime(73#*40+(73#-1))*isprime(73#*40+(73#+1))
41*isprime(73#*41+(73#-1))*isprime(73#*41+(73#+1))
42*isprime(73#*42+(73#-1))*isprime(73#*42+(73#+1))
43*isprime(73#*43+(73#-1))*isprime(73#*43+(73#+1))
44*isprime(73#*44+(73#-1))*isprime(73#*44+(73#+1))
45*isprime(73#*45+(73#-1))*isprime(73#*45+(73#+1))
46*isprime(73#*46+(73#-1))*isprime(73#*46+(73#+1))
47*isprime(73#*47+(73#-1))*isprime(73#*47+(73#+1))
48*isprime(73#*48+(73#-1))*isprime(73#*48+(73#+1))
49*isprime(73#*49+(73#-1))*isprime(73#*49+(73#+1))
50*isprime(73#*50+(73#-1))*isprime(73#*50+(73#+1))
51*isprime(73#*51+(73#-1))*isprime(73#*51+(73#+1))
52*isprime(73#*52+(73#-1))*isprime(73#*52+(73#+1))
53*isprime(73#*53+(73#-1))*isprime(73#*53+(73#+1))
54*isprime(73#*54+(73#-1))*isprime(73#*54+(73#+1))
55*isprime(73#*55+(73#-1))*isprime(73#*55+(73#+1))
56*isprime(73#*56+(73#-1))*isprime(73#*56+(73#+1))
57*isprime(73#*57+(73#-1))*isprime(73#*57+(73#+1))
58*isprime(73#*58+(73#-1))*isprime(73#*58+(73#+1))
59*isprime(73#*59+(73#-1))*isprime(73#*59+(73#+1))
60*isprime(73#*60+(73#-1))*isprime(73#*60+(73#+1))
61*isprime(73#*61+(73#-1))*isprime(73#*61+(73#+1))
62*isprime(73#*62+(73#-1))*isprime(73#*62+(73#+1))
63*isprime(73#*63+(73#-1))*isprime(73#*63+(73#+1))
64*isprime(73#*64+(73#-1))*isprime(73#*64+(73#+1))
65*isprime(73#*65+(73#-1))*isprime(73#*65+(73#+1))
66*isprime(73#*66+(73#-1))*isprime(73#*66+(73#+1))
67*isprime(73#*67+(73#-1))*isprime(73#*67+(73#+1))
68*isprime(73#*68+(73#-1))*isprime(73#*68+(73#+1))
69*isprime(73#*69+(73#-1))*isprime(73#*69+(73#+1))
70*isprime(73#*70+(73#-1))*isprime(73#*70+(73#+1))
71*isprime(73#*71+(73#-1))*isprime(73#*71+(73#+1))
72*isprime(73#*72+(73#-1))*isprime(73#*72+(73#+1))
73*isprime(73#*73+(73#-1))*isprime(73#*73+(73#+1))
74*isprime(73#*74+(73#-1))*isprime(73#*74+(73#+1))
75*isprime(73#*75+(73#-1))*isprime(73#*75+(73#+1))
76*isprime(73#*76+(73#-1))*isprime(73#*76+(73#+1))
77*isprime(73#*77+(73#-1))*isprime(73#*77+(73#+1))
78*isprime(73#*78+(73#-1))*isprime(73#*78+(73#+1))

no twin prime in the range, very normal result
__
range 79# to 83#
only probably 82 twinprime test:
19*isprime(79#*19+(79#-1))*isprime(79#*19+(79#+1))
74*isprime(79#*74+(79#-1))*isprime(79#*74+(79#+1))
n=19,74
2 twinprime.

64352895346813458157981691082599
64352895346813458157981691082599+2
241323357550550468092431341559749
241323357550550468092431341559749+2
32 and 33 decimal digits 2 twin primes!

__
range 83# to 89#
82*isprime(83#*82+(83#-1))*isprime(83#*82+(83#+1))
22166354802209895662516793493401569
22166354802209895662516793493401569+2
35 decimal digits
how is 1 twin prime posible, in the probably 88 twin primes
__
range 89# to 97#
90*isprime(89#*90+(89#-1))*isprime(89#*90+(89#+1))
2162955512567445120129198921723606209
2162955512567445120129198921723606209+2

how is 1 twin prime posible, in the probably 96 twin primes
__
range 97# to 101#
1*isprime(97#*1+(97#-1))*isprime(97#*1+(97#+1))
2*isprime(97#*2+(97#-1))*isprime(97#*2+(97#+1))
3*isprime(97#*3+(97#-1))*isprime(97#*3+(97#+1))
4*isprime(97#*4+(97#-1))*isprime(97#*4+(97#+1))
5*isprime(97#*5+(97#-1))*isprime(97#*5+(97#+1))
6*isprime(97#*6+(97#-1))*isprime(97#*6+(97#+1))
7*isprime(97#*7+(97#-1))*isprime(97#*7+(97#+1))
8*isprime(97#*8+(97#-1))*isprime(97#*8+(97#+1))
9*isprime(97#*9+(97#-1))*isprime(97#*9+(97#+1))
10*isprime(97#*10+(97#-1))*isprime(97#*10+(97#+1))
11*isprime(97#*11+(97#-1))*isprime(97#*11+(97#+1))
12*isprime(97#*12+(97#-1))*isprime(97#*12+(97#+1))
13*isprime(97#*13+(97#-1))*isprime(97#*13+(97#+1))
14*isprime(97#*14+(97#-1))*isprime(97#*14+(97#+1))
15*isprime(97#*15+(97#-1))*isprime(97#*15+(97#+1))
16*isprime(97#*16+(97#-1))*isprime(97#*16+(97#+1))
17*isprime(97#*17+(97#-1))*isprime(97#*17+(97#+1))
18*isprime(97#*18+(97#-1))*isprime(97#*18+(97#+1))
19*isprime(97#*19+(97#-1))*isprime(97#*19+(97#+1))
20*isprime(97#*20+(97#-1))*isprime(97#*20+(97#+1))
21*isprime(97#*21+(97#-1))*isprime(97#*21+(97#+1))
22*isprime(97#*22+(97#-1))*isprime(97#*22+(97#+1))
23*isprime(97#*23+(97#-1))*isprime(97#*23+(97#+1))
24*isprime(97#*24+(97#-1))*isprime(97#*24+(97#+1))
25*isprime(97#*25+(97#-1))*isprime(97#*25+(97#+1))
26*isprime(97#*26+(97#-1))*isprime(97#*26+(97#+1))
27*isprime(97#*27+(97#-1))*isprime(97#*27+(97#+1))
28*isprime(97#*28+(97#-1))*isprime(97#*28+(97#+1))
29*isprime(97#*29+(97#-1))*isprime(97#*29+(97#+1))
30*isprime(97#*30+(97#-1))*isprime(97#*30+(97#+1))
31*isprime(97#*31+(97#-1))*isprime(97#*31+(97#+1))
32*isprime(97#*32+(97#-1))*isprime(97#*32+(97#+1))
33*isprime(97#*33+(97#-1))*isprime(97#*33+(97#+1))
34*isprime(97#*34+(97#-1))*isprime(97#*34+(97#+1))
35*isprime(97#*35+(97#-1))*isprime(97#*35+(97#+1))
36*isprime(97#*36+(97#-1))*isprime(97#*36+(97#+1))
37*isprime(97#*37+(97#-1))*isprime(97#*37+(97#+1))
38*isprime(97#*38+(97#-1))*isprime(97#*38+(97#+1))
39*isprime(97#*39+(97#-1))*isprime(97#*39+(97#+1))
40*isprime(97#*40+(97#-1))*isprime(97#*40+(97#+1))
41*isprime(97#*41+(97#-1))*isprime(97#*41+(97#+1))
42*isprime(97#*42+(97#-1))*isprime(97#*42+(97#+1))
43*isprime(97#*43+(97#-1))*isprime(97#*43+(97#+1))
44*isprime(97#*44+(97#-1))*isprime(97#*44+(97#+1))
45*isprime(97#*45+(97#-1))*isprime(97#*45+(97#+1))
46*isprime(97#*46+(97#-1))*isprime(97#*46+(97#+1))
47*isprime(97#*47+(97#-1))*isprime(97#*47+(97#+1))
48*isprime(97#*48+(97#-1))*isprime(97#*48+(97#+1))
49*isprime(97#*49+(97#-1))*isprime(97#*49+(97#+1))
50*isprime(97#*50+(97#-1))*isprime(97#*50+(97#+1))
51*isprime(97#*51+(97#-1))*isprime(97#*51+(97#+1))
52*isprime(97#*52+(97#-1))*isprime(97#*52+(97#+1))
53*isprime(97#*53+(97#-1))*isprime(97#*53+(97#+1))
54*isprime(97#*54+(97#-1))*isprime(97#*54+(97#+1))
55*isprime(97#*55+(97#-1))*isprime(97#*55+(97#+1))
56*isprime(97#*56+(97#-1))*isprime(97#*56+(97#+1))
57*isprime(97#*57+(97#-1))*isprime(97#*57+(97#+1))
58*isprime(97#*58+(97#-1))*isprime(97#*58+(97#+1))
59*isprime(97#*59+(97#-1))*isprime(97#*59+(97#+1))
60*isprime(97#*60+(97#-1))*isprime(97#*60+(97#+1))
61*isprime(97#*61+(97#-1))*isprime(97#*61+(97#+1))
62*isprime(97#*62+(97#-1))*isprime(97#*62+(97#+1))
63*isprime(97#*63+(97#-1))*isprime(97#*63+(97#+1))
64*isprime(97#*64+(97#-1))*isprime(97#*64+(97#+1))
65*isprime(97#*65+(97#-1))*isprime(97#*65+(97#+1))
66*isprime(97#*66+(97#-1))*isprime(97#*66+(97#+1))
67*isprime(97#*67+(97#-1))*isprime(97#*67+(97#+1))
68*isprime(97#*68+(97#-1))*isprime(97#*68+(97#+1))
69*isprime(97#*69+(97#-1))*isprime(97#*69+(97#+1))
70*isprime(97#*70+(97#-1))*isprime(97#*70+(97#+1))
71*isprime(97#*71+(97#-1))*isprime(97#*71+(97#+1))
72*isprime(97#*72+(97#-1))*isprime(97#*72+(97#+1))
73*isprime(97#*73+(97#-1))*isprime(97#*73+(97#+1))
74*isprime(97#*74+(97#-1))*isprime(97#*74+(97#+1))
75*isprime(97#*75+(97#-1))*isprime(97#*75+(97#+1))
76*isprime(97#*76+(97#-1))*isprime(97#*76+(97#+1))
77*isprime(97#*77+(97#-1))*isprime(97#*77+(97#+1))
78*isprime(97#*78+(97#-1))*isprime(97#*78+(97#+1))
79*isprime(97#*79+(97#-1))*isprime(97#*79+(97#+1))
80*isprime(97#*80+(97#-1))*isprime(97#*80+(97#+1))
81*isprime(97#*81+(97#-1))*isprime(97#*81+(97#+1))
82*isprime(97#*82+(97#-1))*isprime(97#*82+(97#+1))
83*isprime(97#*83+(97#-1))*isprime(97#*83+(97#+1))
84*isprime(97#*84+(97#-1))*isprime(97#*84+(97#+1))
85*isprime(97#*85+(97#-1))*isprime(97#*85+(97#+1))
86*isprime(97#*86+(97#-1))*isprime(97#*86+(97#+1))
87*isprime(97#*87+(97#-1))*isprime(97#*87+(97#+1))
88*isprime(97#*88+(97#-1))*isprime(97#*88+(97#+1))
89*isprime(97#*89+(97#-1))*isprime(97#*89+(97#+1))
90*isprime(97#*90+(97#-1))*isprime(97#*90+(97#+1))
91*isprime(97#*91+(97#-1))*isprime(97#*91+(97#+1))
92*isprime(97#*92+(97#-1))*isprime(97#*92+(97#+1))
93*isprime(97#*93+(97#-1))*isprime(97#*93+(97#+1))
94*isprime(97#*94+(97#-1))*isprime(97#*94+(97#+1))
95*isprime(97#*95+(97#-1))*isprime(97#*95+(97#+1))
96*isprime(97#*96+(97#-1))*isprime(97#*96+(97#+1))
97*isprime(97#*97+(97#-1))*isprime(97#*97+(97#+1))
98*isprime(97#*98+(97#-1))*isprime(97#*98+(97#+1))
99*isprime(97#*99+(97#-1))*isprime(97#*99+(97#+1))
100*isprime(97#*100+(97#-1))*isprime(97#*100+(97#+1))

n=34
34*isprime(97#*34+(97#-1))*isprime(97#*34+(97#+1))
and
n=71
71*isprime(97#*71+(97#-1))*isprime(97#*71+(97#+1))
166000893404077326582223354607886437039
166000893404077326582223354607886437041

80694878738093144866358575156611462449
80694878738093144866358575156611462451
__
i love this tests.
...
...
nextprime(1e4#) to nextprime(nextprime(1e4#)) test yourself.
for examples:
1*isprime(179#*1+(179#-1))*isprime(179#*1+(179#+1))
2*isprime(179#*2+(179#-1))*isprime(179#*2+(179#+1))
3*isprime(179#*3+(179#-1))*isprime(179#*3+(179#+1))
4*isprime(179#*4+(179#-1))*isprime(179#*4+(179#+1))
5*isprime(179#*5+(179#-1))*isprime(179#*5+(179#+1))
6*isprime(179#*6+(179#-1))*isprime(179#*6+(179#+1))
7*isprime(179#*7+(179#-1))*isprime(179#*7+(179#+1))
8*isprime(179#*8+(179#-1))*isprime(179#*8+(179#+1))
9*isprime(179#*9+(179#-1))*isprime(179#*9+(179#+1))
10*isprime(179#*10+(179#-1))*isprime(179#*10+(179#+1))
11*isprime(179#*11+(179#-1))*isprime(179#*11+(179#+1))
12*isprime(179#*12+(179#-1))*isprime(179#*12+(179#+1))
13*isprime(179#*13+(179#-1))*isprime(179#*13+(179#+1))
14*isprime(179#*14+(179#-1))*isprime(179#*14+(179#+1))
15*isprime(179#*15+(179#-1))*isprime(179#*15+(179#+1))
16*isprime(179#*16+(179#-1))*isprime(179#*16+(179#+1))
17*isprime(179#*17+(179#-1))*isprime(179#*17+(179#+1))
18*isprime(179#*18+(179#-1))*isprime(179#*18+(179#+1))
19*isprime(179#*19+(179#-1))*isprime(179#*19+(179#+1))
20*isprime(179#*20+(179#-1))*isprime(179#*20+(179#+1))
21*isprime(179#*21+(179#-1))*isprime(179#*21+(179#+1))
22*isprime(179#*22+(179#-1))*isprime(179#*22+(179#+1))
23*isprime(179#*23+(179#-1))*isprime(179#*23+(179#+1))
24*isprime(179#*24+(179#-1))*isprime(179#*24+(179#+1))
25*isprime(179#*25+(179#-1))*isprime(179#*25+(179#+1))
26*isprime(179#*26+(179#-1))*isprime(179#*26+(179#+1))
27*isprime(179#*27+(179#-1))*isprime(179#*27+(179#+1))
28*isprime(179#*28+(179#-1))*isprime(179#*28+(179#+1))
29*isprime(179#*29+(179#-1))*isprime(179#*29+(179#+1))
30*isprime(179#*30+(179#-1))*isprime(179#*30+(179#+1))
31*isprime(179#*31+(179#-1))*isprime(179#*31+(179#+1))
32*isprime(179#*32+(179#-1))*isprime(179#*32+(179#+1))
33*isprime(179#*33+(179#-1))*isprime(179#*33+(179#+1))
34*isprime(179#*34+(179#-1))*isprime(179#*34+(179#+1))
35*isprime(179#*35+(179#-1))*isprime(179#*35+(179#+1))
36*isprime(179#*36+(179#-1))*isprime(179#*36+(179#+1))
37*isprime(179#*37+(179#-1))*isprime(179#*37+(179#+1))
38*isprime(179#*38+(179#-1))*isprime(179#*38+(179#+1))
39*isprime(179#*39+(179#-1))*isprime(179#*39+(179#+1))
40*isprime(179#*40+(179#-1))*isprime(179#*40+(179#+1))
41*isprime(179#*41+(179#-1))*isprime(179#*41+(179#+1))
42*isprime(179#*42+(179#-1))*isprime(179#*42+(179#+1))
43*isprime(179#*43+(179#-1))*isprime(179#*43+(179#+1))
44*isprime(179#*44+(179#-1))*isprime(179#*44+(179#+1))
45*isprime(179#*45+(179#-1))*isprime(179#*45+(179#+1))
46*isprime(179#*46+(179#-1))*isprime(179#*46+(179#+1))
47*isprime(179#*47+(179#-1))*isprime(179#*47+(179#+1))
48*isprime(179#*48+(179#-1))*isprime(179#*48+(179#+1))
49*isprime(179#*49+(179#-1))*isprime(179#*49+(179#+1))
50*isprime(179#*50+(179#-1))*isprime(179#*50+(179#+1))
51*isprime(179#*51+(179#-1))*isprime(179#*51+(179#+1))
52*isprime(179#*52+(179#-1))*isprime(179#*52+(179#+1))
53*isprime(179#*53+(179#-1))*isprime(179#*53+(179#+1))
54*isprime(179#*54+(179#-1))*isprime(179#*54+(179#+1))
55*isprime(179#*55+(179#-1))*isprime(179#*55+(179#+1))
56*isprime(179#*56+(179#-1))*isprime(179#*56+(179#+1))
57*isprime(179#*57+(179#-1))*isprime(179#*57+(179#+1))
58*isprime(179#*58+(179#-1))*isprime(179#*58+(179#+1))
59*isprime(179#*59+(179#-1))*isprime(179#*59+(179#+1))
60*isprime(179#*60+(179#-1))*isprime(179#*60+(179#+1))
61*isprime(179#*61+(179#-1))*isprime(179#*61+(179#+1))
62*isprime(179#*62+(179#-1))*isprime(179#*62+(179#+1))
63*isprime(179#*63+(179#-1))*isprime(179#*63+(179#+1))
64*isprime(179#*64+(179#-1))*isprime(179#*64+(179#+1))
65*isprime(179#*65+(179#-1))*isprime(179#*65+(179#+1))
66*isprime(179#*66+(179#-1))*isprime(179#*66+(179#+1))
67*isprime(179#*67+(179#-1))*isprime(179#*67+(179#+1))
68*isprime(179#*68+(179#-1))*isprime(179#*68+(179#+1))
69*isprime(179#*69+(179#-1))*isprime(179#*69+(179#+1))
70*isprime(179#*70+(179#-1))*isprime(179#*70+(179#+1))
71*isprime(179#*71+(179#-1))*isprime(179#*71+(179#+1))
72*isprime(179#*72+(179#-1))*isprime(179#*72+(179#+1))
73*isprime(179#*73+(179#-1))*isprime(179#*73+(179#+1))
74*isprime(179#*74+(179#-1))*isprime(179#*74+(179#+1))
75*isprime(179#*75+(179#-1))*isprime(179#*75+(179#+1))
76*isprime(179#*76+(179#-1))*isprime(179#*76+(179#+1))
77*isprime(179#*77+(179#-1))*isprime(179#*77+(179#+1))
78*isprime(179#*78+(179#-1))*isprime(179#*78+(179#+1))
79*isprime(179#*79+(179#-1))*isprime(179#*79+(179#+1))
80*isprime(179#*80+(179#-1))*isprime(179#*80+(179#+1))
81*isprime(179#*81+(179#-1))*isprime(179#*81+(179#+1))
82*isprime(179#*82+(179#-1))*isprime(179#*82+(179#+1))
83*isprime(179#*83+(179#-1))*isprime(179#*83+(179#+1))
84*isprime(179#*84+(179#-1))*isprime(179#*84+(179#+1))
85*isprime(179#*85+(179#-1))*isprime(179#*85+(179#+1))
86*isprime(179#*86+(179#-1))*isprime(179#*86+(179#+1))
87*isprime(179#*87+(179#-1))*isprime(179#*87+(179#+1))
88*isprime(179#*88+(179#-1))*isprime(179#*88+(179#+1))
89*isprime(179#*89+(179#-1))*isprime(179#*89+(179#+1))
90*isprime(179#*90+(179#-1))*isprime(179#*90+(179#+1))
91*isprime(179#*91+(179#-1))*isprime(179#*91+(179#+1))
92*isprime(179#*92+(179#-1))*isprime(179#*92+(179#+1))
93*isprime(179#*93+(179#-1))*isprime(179#*93+(179#+1))
94*isprime(179#*94+(179#-1))*isprime(179#*94+(179#+1))
95*isprime(179#*95+(179#-1))*isprime(179#*95+(179#+1))
96*isprime(179#*96+(179#-1))*isprime(179#*96+(179#+1))
97*isprime(179#*97+(179#-1))*isprime(179#*97+(179#+1))
98*isprime(179#*98+(179#-1))*isprime(179#*98+(179#+1))
99*isprime(179#*99+(179#-1))*isprime(179#*99+(179#+1))
100*isprime(179#*100+(179#-1))*isprime(179#*100+(179#+1))
101*isprime(179#*101+(179#-1))*isprime(179#*101+(179#+1))
102*isprime(179#*102+(179#-1))*isprime(179#*102+(179#+1))
103*isprime(179#*103+(179#-1))*isprime(179#*103+(179#+1))
104*isprime(179#*104+(179#-1))*isprime(179#*104+(179#+1))
105*isprime(179#*105+(179#-1))*isprime(179#*105+(179#+1))
106*isprime(179#*106+(179#-1))*isprime(179#*106+(179#+1))
107*isprime(179#*107+(179#-1))*isprime(179#*107+(179#+1))
108*isprime(179#*108+(179#-1))*isprime(179#*108+(179#+1))
109*isprime(179#*109+(179#-1))*isprime(179#*109+(179#+1))
110*isprime(179#*110+(179#-1))*isprime(179#*110+(179#+1))
111*isprime(179#*111+(179#-1))*isprime(179#*111+(179#+1))
112*isprime(179#*112+(179#-1))*isprime(179#*112+(179#+1))
113*isprime(179#*113+(179#-1))*isprime(179#*113+(179#+1))
114*isprime(179#*114+(179#-1))*isprime(179#*114+(179#+1))
115*isprime(179#*115+(179#-1))*isprime(179#*115+(179#+1))
116*isprime(179#*116+(179#-1))*isprime(179#*116+(179#+1))
117*isprime(179#*117+(179#-1))*isprime(179#*117+(179#+1))
118*isprime(179#*118+(179#-1))*isprime(179#*118+(179#+1))
119*isprime(179#*119+(179#-1))*isprime(179#*119+(179#+1))
120*isprime(179#*120+(179#-1))*isprime(179#*120+(179#+1))
121*isprime(179#*121+(179#-1))*isprime(179#*121+(179#+1))
122*isprime(179#*122+(179#-1))*isprime(179#*122+(179#+1))
123*isprime(179#*123+(179#-1))*isprime(179#*123+(179#+1))
124*isprime(179#*124+(179#-1))*isprime(179#*124+(179#+1))
125*isprime(179#*125+(179#-1))*isprime(179#*125+(179#+1))
126*isprime(179#*126+(179#-1))*isprime(179#*126+(179#+1))
127*isprime(179#*127+(179#-1))*isprime(179#*127+(179#+1))
128*isprime(179#*128+(179#-1))*isprime(179#*128+(179#+1))
129*isprime(179#*129+(179#-1))*isprime(179#*129+(179#+1))
130*isprime(179#*130+(179#-1))*isprime(179#*130+(179#+1))
131*isprime(179#*131+(179#-1))*isprime(179#*131+(179#+1))
132*isprime(179#*132+(179#-1))*isprime(179#*132+(179#+1))
133*isprime(179#*133+(179#-1))*isprime(179#*133+(179#+1))
134*isprime(179#*134+(179#-1))*isprime(179#*134+(179#+1))
135*isprime(179#*135+(179#-1))*isprime(179#*135+(179#+1))
136*isprime(179#*136+(179#-1))*isprime(179#*136+(179#+1))
137*isprime(179#*137+(179#-1))*isprime(179#*137+(179#+1))
138*isprime(179#*138+(179#-1))*isprime(179#*138+(179#+1))
139*isprime(179#*139+(179#-1))*isprime(179#*139+(179#+1))
140*isprime(179#*140+(179#-1))*isprime(179#*140+(179#+1))
141*isprime(179#*141+(179#-1))*isprime(179#*141+(179#+1))
142*isprime(179#*142+(179#-1))*isprime(179#*142+(179#+1))
143*isprime(179#*143+(179#-1))*isprime(179#*143+(179#+1))
144*isprime(179#*144+(179#-1))*isprime(179#*144+(179#+1))
145*isprime(179#*145+(179#-1))*isprime(179#*145+(179#+1))
146*isprime(179#*146+(179#-1))*isprime(179#*146+(179#+1))
147*isprime(179#*147+(179#-1))*isprime(179#*147+(179#+1))
148*isprime(179#*148+(179#-1))*isprime(179#*148+(179#+1))
149*isprime(179#*149+(179#-1))*isprime(179#*149+(179#+1))
150*isprime(179#*150+(179#-1))*isprime(179#*150+(179#+1))
151*isprime(179#*151+(179#-1))*isprime(179#*151+(179#+1))
152*isprime(179#*152+(179#-1))*isprime(179#*152+(179#+1))
153*isprime(179#*153+(179#-1))*isprime(179#*153+(179#+1))
154*isprime(179#*154+(179#-1))*isprime(179#*154+(179#+1))
155*isprime(179#*155+(179#-1))*isprime(179#*155+(179#+1))
156*isprime(179#*156+(179#-1))*isprime(179#*156+(179#+1))
157*isprime(179#*157+(179#-1))*isprime(179#*157+(179#+1))
158*isprime(179#*158+(179#-1))*isprime(179#*158+(179#+1))
159*isprime(179#*159+(179#-1))*isprime(179#*159+(179#+1))
160*isprime(179#*160+(179#-1))*isprime(179#*160+(179#+1))
161*isprime(179#*161+(179#-1))*isprime(179#*161+(179#+1))
162*isprime(179#*162+(179#-1))*isprime(179#*162+(179#+1))
163*isprime(179#*163+(179#-1))*isprime(179#*163+(179#+1))
164*isprime(179#*164+(179#-1))*isprime(179#*164+(179#+1))
165*isprime(179#*165+(179#-1))*isprime(179#*165+(179#+1))
166*isprime(179#*166+(179#-1))*isprime(179#*166+(179#+1))
167*isprime(179#*167+(179#-1))*isprime(179#*167+(179#+1))
168*isprime(179#*168+(179#-1))*isprime(179#*168+(179#+1))
169*isprime(179#*169+(179#-1))*isprime(179#*169+(179#+1))
170*isprime(179#*170+(179#-1))*isprime(179#*170+(179#+1))
171*isprime(179#*171+(179#-1))*isprime(179#*171+(179#+1))
172*isprime(179#*172+(179#-1))*isprime(179#*172+(179#+1))
173*isprime(179#*173+(179#-1))*isprime(179#*173+(179#+1))
174*isprime(179#*174+(179#-1))*isprime(179#*174+(179#+1))
175*isprime(179#*175+(179#-1))*isprime(179#*175+(179#+1))
176*isprime(179#*176+(179#-1))*isprime(179#*176+(179#+1))
177*isprime(179#*177+(179#-1))*isprime(179#*177+(179#+1))
178*isprime(179#*178+(179#-1))*isprime(179#*178+(179#+1))
179*isprime(179#*179+(179#-1))*isprime(179#*179+(179#+1))
180*isprime(179#*180+(179#-1))*isprime(179#*180+(179#+1))

n=172 twin prime!
172*isprime(179#*172+(179#-1))*isprime(179#*172+(179#+1))

(179#*172+(179#-1))
(179#*172+(179#+1))

5158789550582100068566834449931204367324113440624489853008262468109349569 (73 decimal digits) is prime
5158789550582100068566834449931204367324113440624489853008262468109349571 (73 decimal digits) is prime

180*2=360 probably prime test only 1200 miliseconds=~ 1 second
but easy find 1 twinprime!
important question?
how is it?
prime template's last probably twin prime elements, twin prime count greater than 0 posibilities, bigger than normal distribition posibilities?
this is important question, don't forget!
if anyone answer and proofed this question, easy proofed infinity twin primes there are!
math very simple!
if some think and if look full picture!

 hal1se 2018-08-30 08:50

what is posibilies?

79*isprime(101#*79+(101#-1))*isprime(101#*79+(101#+1))
47*isprime(103#*47+(103#-1))*isprime(103#*47+(103#+1))
46*isprime(107#*46+(107#-1))*isprime(107#*46+(107#+1))
1*isprime(113#*1+(113#-1))*isprime(113#*1+(113#+1))
11*isprime(127#*11+(127#-1))*isprime(127#*11+(127#+1))
29*isprime(137#*29+(137#-1))*isprime(137#*29+(137#+1))
53*isprime(151#*53+(151#-1))*isprime(151#*53+(151#+1))
59*isprime(151#*59+(151#-1))*isprime(151#*59+(151#+1))
107*isprime(163#*107+(163#-1))*isprime(163#*107+(163#+1))
172*isprime(179#*172+(179#-1))*isprime(179#*172+(179#+1))
12*isprime(193#*12+(193#-1))*isprime(193#*12+(193#+1))
172*isprime(227#*172+(227#-1))*isprime(227#*172+(227#+1))
68*isprime(257#*68+(257#-1))*isprime(257#*68+(257#+1))
120*isprime(263#*120+(263#-1))*isprime(263#*120+(263#+1))
35*isprime(277#*35+(277#-1))*isprime(277#*35+(277#+1))
__
(277#*35+(277#-1))
(277#*35+(277#+1))
3157738909381382798745796947067407592867578860122933360095448333290935384829812781822776257744020941448521031830039
3157738909381382798745796947067407592867578860122933360095448333290935384829812781822776257744020941448521031830041
115 decimal digits twinprime count=1 posibilities from 280 probably twins?
what is posibilities, real twin count >0 from prime template's last element probably twin primes?
this posibilities > normal distribition posibilities!
__
169*isprime(283#*169+(283#-1))*isprime(283#*169+(283#+1))
203*isprime(293#*203+(293#-1))*isprime(293#*203+(293#+1))
284*isprime(307#*284+(307#-1))*isprime(307#*284+(307#+1))
246*isprime(313#*246+(313#-1))*isprime(313#*246+(313#+1))
104*isprime(347#*104+(347#-1))*isprime(347#*104+(347#+1))
292*isprime(347#*292+(347#-1))*isprime(347#*292+(347#+1))
__
347#*104+(347#-+1)
347#*292+(347#-+1)

7868883694105963077478274378618356797758218387401816932316269834340593371693121233072845496377529219422653670780988755

5784309435133443838649 (140 decimal digits) is prime
7868883694105963077478274378618356797758218387401816932316269834340593371693121233072845496377529219422653670780988755

5784309435133443838651 (140 decimal digits) is prime

2195793259402902077810604183747789087374436178579745105874921010915994150386747163133660695655824820276988119560790195

60426692042800943283089 (141 decimal digits) is prime
2195793259402902077810604183747789087374436178579745105874921010915994150386747163133660695655824820276988119560790195

60426692042800943283091 (141 decimal digits) is prime

what is posibilities, about 140 decimal digits twin primes count=2, from 348 probably twins?
__
i am boring, this tests!
i will go to holiday, i.

 Batalov 2018-08-30 14:38

Look here [URL]http://primes.utm.edu/top20/page.php?id=1[/URL]
and stop yanking everyone's sleeves about 140-digit primes.

 paulunderwood 2018-08-30 14:46

Also, a collaboration of the world's greatest mathematicians have made an attempt on [URL="https://en.wikipedia.org/wiki/Twin_prime"]The Twin Prime Conjecture[/URL]: [url]https://en.wikipedia.org/wiki/Polymath_Project#Polymath8[/url]. I really think you will get absolutely no where new (especially with long boring lists of computer output).

 Xyzzy 2018-08-30 16:14

Any post longer than a screen is immediately skipped by us, and maybe most others?

:mike:

 chalsall 2018-08-30 16:27

[QUOTE=Xyzzy;494947]Any post longer than a screen is immediately skipped by us, and maybe most others?[/QUOTE]

Less is more.

 Collag3n 2018-08-31 07:45

The symmetry and regularity found in the primorials [TEX]p_a[/TEX]# when you sieve up to the [TEX]a^{th}[/TEX] prime is well known. The count can be derived from the Euler totient formula: [TEX](3-1)(5-1)(7-1)(11-1)....(p_a-1)[/TEX].

The same count can be done for twins: the 1,3,15,135,.... you found which comes from the same kind of formulas: [TEX](3-2)(5-2)(7-2)(11-2)....(p_a-2)[/TEX].

Unfortunately, this is not enough to prove infinity. You have to prove that they are not all sieved by subsequent [TEX]p_a[/TEX]. And this can't be done with probabilities.

 hal1se 2018-08-31 13:12

infinity ranges, at least 1 twin count.

347# to 349#
range :349#-347#=347#*(349-1)
middle point of range=(347#+349#)/2=347#*(1+349)/2
range rough twin count=(4/3)*range/(ln(middle point of range)) ^2 =
(4/3)*2,60797288e140/(322,63306975911838731774988255887)^2
=3,341e+135

347# template probably twin elements:
9,002380832605367660054087978901062006539085458962789840394506950149331_..
.._553222941092693963879642982711996155339023418711102008819580078125e+135

prime template's last probably twin prime elemens, twin count probabilities average=

3,341e+135/9,00238e+135=0,37 (0,37 only this range, for example 5# to 7# average probabiliy=3,3)

twin count=2 near 0,37 average probabiliy.
twin count=0 normal
but
twin count=1,2,...,7 normal again!
but twin count=17 not normal!

every prime template's probably twin element (last element or any probably twin element) average probabilities = ?

for example:
347# to 349# ranges twin count > 1e135
but we look only this time: at least 1 twin count, in the range.

question:
average probabilites > 0 allways?
we don't use, template probably twin element count!
we don't use, premorial range rough count!
but easy prof, still:
if some one, answer and proofed, every prime template's probably twin element, average probabilites > 0 allways then:

infinity ranges, at least 1 twin count.
you must look hypergeometric and think complex variable domains.
easy proof, don't forget!
math very simple.

 hal1se 2018-09-02 03:37

your calc. only:1,902 only 3 digit after comma!

[FONT="Courier New"][SIZE="3"][QUOTE=paulunderwood;494939]Also, a collaboration of the world's greatest mathematicians have made an attempt on [URL="https://en.wikipedia.org/wiki/Twin_prime"]The Twin Prime Conjecture[/URL]: [url]https://en.wikipedia.org/wiki/Polymath_Project#Polymath8[/url].[COLOR="SeaGreen"] I really think [/COLOR]you will get absolutely no where new (especially with long boring lists of computer output).[/QUOTE]

[url]http://www.britannica.com/science/twin-prime-conjecture[/url]
In 2010 Nicely gave a value for Brun’s constant of
1.902160583209 ± 0.000000000781 based on all twin primes less than 2 × 10^16
0.000000000781
__123456789012
1,902160583209+0,000000000781=
1,90216058399
1,902160583209-0,000000000781=
1,902160582428 **
__12345678
8 digit after comma!
range 2e16 to 1e17
real prime count:2075693725704225
ln(middle point of range)=
=ln((2e16+1e17)/2)=ln(6e16)=38,633120957132785945100340633331
rough twin count=
=1,3219*(2075693725704225/38,633120957132785945100340633331=
=71023501804397 -+(%0,3)
1/1e17+1/1e17: last twin , 2 prime about reciprocity
71023501804397*2/1e17=0,001420
0,001420
__123
3th digit after comma :1
1,902160582428 **
__12345678
4. digit after comma not meanfull!
so:
1,902 only true!
if some one say, your calc. rough!
not important rough!
we use last range element:2*1/1e17
but 2*2/1e16 to 2*1/1e17 elements sum>71023501804397*2/1e17
so, may be:0,001420 up to another great number!
but 2. digit not wrong.
only 4. and may be 3. digit after comma false!
very clear![/SIZE][/FONT]

 hal1se 2018-09-02 04:29

[QUOTE=hal1se;495154][FONT="Courier New"][SIZE="3"]

but 2*2/1e16 to 2*1/1e17 elements sum>71023501804397*2/1e17[/SIZE][/FONT][/QUOTE]

sory, my brain damage!
2/2e16 to 2/1e17 reciproc element sum>71023501804397*2/1e17

this brun sum, must be at least : 128 bit computer, and:
2^128 /2= ~ 38 decimal floating point.
38 flating point calc.: from 3 to 1e29, at least 3 to 1e23
___
if some one any idea show:
for example:
any primorial range at least 1 twin count analysis, how method show?
my 'computer' output only for people think!

"find easy twin, in inifinty twin" only teoric find easy infinity twin, so proofed infinity twin!
but many people not understand my idea, not look large perspective!
many pepole think: primes: only positive real integers!
if many people not understand and can not large think!
may be: must be this is reality!

 Batalov 2018-09-02 06:20

1 Attachment(s)
[QUOTE=hal1se;495156]if many people not understand and can not large think!
[/QUOTE]
Look, Ma! No hands!!

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