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Forum: sweety439 2020-11-27, 16:41
Replies: 363
Views: 13,505
Posted By sweety439
Update files for unique primes

Update files for unique primes
Forum: Miscellaneous Math 2020-11-27, 05:57
Replies: 15
Views: 210
Posted By sweety439
This number has trivial 50% N-1 factorization. ...

This number has trivial 50% N-1 factorization.

What is the largest number proven to be prime by N-1 / N+1 / combined methods, but without trivial factorization (i.e. N-1 / N+1 is not divisible by...
Forum: sweety439 2020-11-27, 05:44
Replies: 20
Views: 520
Posted By sweety439
Links for Aliquot sequence: ...

Links for Aliquot sequence:

http://www.aliquot.de/aliquote.htm
http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html
http://www.aliquotes.com/...
Forum: sweety439 2020-11-27, 05:34
Replies: 20
Views: 520
Posted By sweety439
http://www.ellipsa.eu/ https://primes.utm.edu/ ...

http://www.ellipsa.eu/
https://primes.utm.edu/
https://primes.utm.edu/curios/home.php
https://www.ellipsa.eu/public/primo/top20.html
http://www.primerecords.dk/
https://www.primepuzzles.net/...
Forum: sweety439 2020-11-27, 05:27
Replies: 20
Views: 520
Posted By sweety439
Prime programs: PARI/GP...

Prime programs:

PARI/GP (http://pari.math.u-bordeaux.fr/)
PRIMO (http://www.ellipsa.eu/public/primo/primo.html)
PFGW (https://sourceforge.net/projects/openpfgw/)
LLR...
Forum: sweety439 2020-11-27, 05:25
Replies: 20
Views: 520
Posted By sweety439
https://members.loria.fr/PZimmermann/records/ecmne...

https://members.loria.fr/PZimmermann/records/ecmnet.html
http://www.rechenkraft.net/yoyo/
https://escatter11.fullerton.edu/nfs/
http://home.iprimus.com.au/bobb777/...
Forum: sweety439 2020-11-27, 05:16
Replies: 20
Views: 520
Posted By sweety439
http://myfactors.mooo.com/ http://factordb.com/...

http://myfactors.mooo.com/
http://factordb.com/
https://stdkmd.net/nrr/repunit/
http://www.primenumbers.net/prptop/prptop.php/
https://primes.utm.edu/primes/lists/all.txt...
Forum: sweety439 2020-11-27, 05:07
Replies: 20
Views: 520
Posted By sweety439
Links for repunit: ...

Links for repunit:

http://www.kurtbeschorner.de/
https://maths-people.anu.edu.au/~brent/factors.html
https://gmplib.org/~tege/repunit.html
https://repunit-koide.jimdo.com/...
Forum: sweety439 2020-11-26, 16:20
Replies: 68
Views: 5,749
Posted By sweety439
Update the sieve files for the "minimal primes...

Update the sieve files for the "minimal primes problem" in base 36
Forum: sweety439 2020-11-26, 04:41
Replies: 68
Views: 5,749
Posted By sweety439
There are still these families: *...

There are still these families:

* x:{0}:(69-x):y:49 (both x and y are divisible by 7)
* x:{0}:y:(69-x):49 (both x and y are divisible by 7)
* 46:46:{42}:49
* x:46:{42}:49 (x is divisible by 7)...
Forum: sweety439 2020-11-26, 04:36
Replies: 68
Views: 5,749
Posted By sweety439
Other possible such simple families: (since...

Other possible such simple families: (since x:0:(69-x):49 has trivial factor of 59)

x:{0}:(69-x):(69-x):49


14,3225349
21,176989
28,47394646445260800000000000150109
35,250489
42,32659298869
Forum: sweety439 2020-11-26, 04:25
Replies: 68
Views: 5,749
Posted By sweety439
minimal primes in base 60 up to 2^32...

minimal primes in base 60 up to 2^32 (https://raw.githubusercontent.com/xayahrainie4793/primes/master/kernel60.txt)
Forum: sweety439 2020-11-26, 04:18
Replies: 68
Views: 5,749
Posted By sweety439
14:{0}:x:49 ...

14:{0}:x:49


1,24253982091278071092686802139899494400000000000000000000000000000000000000000109
2,1009
3,1069
4,1129
5,3024349
6,1249
8,50929
Forum: sweety439 2020-11-26, 02:41
Replies: 68
Views: 5,749
Posted By sweety439
Other possible such simple families: ...

Other possible such simple families:

10:10:{0}:49

prime is 2196049

58:58:{0}:1

prime is 212281
Forum: sweety439 2020-11-26, 02:39
Replies: 68
Views: 5,749
Posted By sweety439
{49}:x:49 1,176509 2,10760569 ...

{49}:x:49


1,176509
2,10760569
3,176629
4,645800689
5,1807836177355932200749
6,176809
8,8369611932200929
Forum: sweety439 2020-11-26, 02:35
Replies: 68
Views: 5,749
Posted By sweety439
x:{14}:49 1,109 2,8089 3,229 ...

x:{14}:49


1,109
2,8089
3,229
4,15289
5,349
6,409
8,1779289
Forum: sweety439 2020-11-26, 02:28
Replies: 68
Views: 5,749
Posted By sweety439
Smallest prime in given simple family in base 60:...

Smallest prime in given simple family in base 60:

{x}:1


1,61
2,7321
3,181
4,241
5,18301
Forum: sweety439 2020-11-26, 02:23
Replies: 68
Views: 5,749
Posted By sweety439
46:{42}:49 family has trivial factor of 53, thus...

46:{42}:49 family has trivial factor of 53, thus not need to be checked.

Also checked these families:

* 10:10:{0}:49
* 10:x:{0}:49 (x = 14, 21, 28, 35, 42, 49)
* x:10:{0}:49 (x = 14, 21, 28,...
Forum: sweety439 2020-11-25, 15:18
Replies: 1,112
Views: 42,073
Posted By sweety439
The reason for (k=27 is excluded from S8) (k=4 is...

The reason for (k=27 is excluded from S8) (k=4 is excluded from S16) (k=1 is excluded from R4) (k=1 is excluded from R8) is the same as (k=1 is excluded from CRUS R14) (k=1 is excluded from CRUS R20)
Forum: sweety439 2020-11-25, 15:14
Replies: 68
Views: 5,749
Posted By sweety439
For the minimal problem in base 60, I checked...

For the minimal problem in base 60, I checked these families: (x is any given digit)

* x:{0}:1
* x:{0}:49 (x not divisible by 7, x != 10)
* {x}:1
* {x}:49 (x not divisible by 7)
* x:{49} (x...
Forum: sweety439 2020-11-25, 14:56
Replies: 68
Views: 5,749
Posted By sweety439
The lower bound of the largest minimal prime in...

The lower bound of the largest minimal prime in base 60 is e19371, also Q8961 is minimal prime in base 60

The values of them are...
Forum: Abstract Algebra & Algebraic Number Theory 2020-11-25, 14:09
Replies: 1
Views: 41
Posted By sweety439
the page only writes "trivial density O(ln(N))",...

the page only writes "trivial density O(ln(N))", however, I know that the density is different by triple (k,b,c), e.g. 29*2^n-1 has much low density as 17*2^n-1
Forum: Abstract Algebra & Algebraic Number Theory 2020-11-25, 14:07
Replies: 1
Views: 41
Posted By sweety439
Excepted number of primes of the form (k*b^n+c)/gcd(k+c,b-1) for n <= given number

According to the page https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Tables_of_special_primes, the excepted number of primes of the polynomial function form a0+a1n+a2n2+a3n3+a4n4+...+arnr (with...
Forum: sweety439 2020-11-25, 08:50
Replies: 68
Views: 5,749
Posted By sweety439
In Sierpinski problem...

In Sierpinski problem (http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm) base b, the prime for a k-value <b is "minimal prime base b" if and only if k is not prime.

In Riesel problem...
Forum: sweety439 2020-11-25, 08:43
Replies: 68
Views: 5,749
Posted By sweety439
The smallest generalized repunit prime in base b...

The smallest generalized repunit prime in base b (if exists) is always minimal prime in base b, since it is 111...111 in base b

Thus, a given base b which is not perfect power (of the form m^r...
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