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Old 2019-11-27, 09:42   #23
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Quote:
Originally Posted by sweety439 View Post
A (probable) prime was found:

(13998*40^12381+29)/13

Written in base 40, this number is Qa{U12380}X

This number is likely the second-largest "base 40 minimal prime"
(86*40^n+37)/3 (S{Q}d in base 40) currently at n=21939, no (probable) prime found.

(4428*36^n+67)/5 (O{L}Z in base 36) currently at n=23729, no (probable) prime found.

(6480*36^n+821)/7 ({P}SZ in base 36) currently at n=20235, no (probable) prime found.
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Old 2019-11-27, 21:37   #24
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Quote:
Originally Posted by sweety439 View Post
(86*40^n+37)/3 (S{Q}d in base 40) currently at n=21939, no (probable) prime found.

(4428*36^n+67)/5 (O{L}Z in base 36) currently at n=23729, no (probable) prime found.

(6480*36^n+821)/7 ({P}SZ in base 36) currently at n=20235, no (probable) prime found.
(86*40^n+37)/3 (S{Q}d in base 40) tested to n=25K, no (probable) prime found.

Extended to n=50K
Attached Files
File Type: txt status for base 40 SQQQQQQd family.txt (66.1 KB, 29 views)
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Old 2019-11-27, 21:40   #25
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(4428*36^n+67)/5 (O{L}Z in base 36) currently at n=32401, no (probable) prime found.

(6480*36^n+821)/7 ({P}SZ in base 36) currently at n=26743, no (probable) prime found.
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Old 2019-11-27, 21:46   #26
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Quote:
Originally Posted by sweety439 View Post
A (probable) prime was found:

(13998*40^12381+29)/13

Written in base 40, this number is Qa{U12380}X

This number is likely the second-largest "base 40 minimal prime"
See the page https://github.com/RaymondDevillers/primes
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Old 2019-11-27, 21:51   #27
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Quote:
Originally Posted by sweety439 View Post
(86*40^n+37)/3 (S{Q}d in base 40) tested to n=25K, no (probable) prime found.

Extended to n=50K
(86*40^n+37)/3 (S{Q}d in base 40) seems to have a low weight, for 25K<=n<=50K, sieve to p=10^9, only 481 n remain.

Last fiddled with by sweety439 on 2019-11-27 at 21:51
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Old 2019-11-27, 22:41   #28
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Quote:
Originally Posted by sweety439 View Post
(4428*36^n+67)/5 (O{L}Z in base 36) currently at n=32401, no (probable) prime found.

(6480*36^n+821)/7 ({P}SZ in base 36) currently at n=26743, no (probable) prime found.
I know that they can be reduced to (123*36^n+67)/5 and (5*36^n+821)/7, however, we let n be the number of the digits in "{}" (thus, the base 40 unsolved family should be (3440*40^n+37)/3 ....

Last fiddled with by sweety439 on 2019-11-27 at 22:42
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Old 2019-11-28, 02:37   #29
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We assume the conjecture in post https://mersenneforum.org/showpost.p...&postcount=675 is true (thus, all families in the files "unsolved xx" in https://github.com/curtisbright/mepn...ee/master/data and all families in the files "left xx" in https://github.com/RaymondDevillers/primes have infinitely many primes)

Then the number of base n digits of the largest base n minimal prime is about 2^eulerphi(n)

Code:
 n length of the largest minimal prime in base n
 2 2
 3 3
 4 2
 5 5
 6 5
 7 5
 8 9
 9 4
10 8
11 45
12 8
13 32021 (PRP)
14 86
15 107
16 3545
18 33
20 449
22 764
23 800874 (PRP)
24 100
30 1024
42 487
Code:
 n excepted length of the largest minimal prime in base n
 2 2
 3 4
 4 4
 5 16
 6 4
 7 64
 8 16
 9 64
10 16
11 1024
12 16
13 4096
14 64
15 256
16 256
17 65536
18 64
19 262144
20 256
21 4096
22 1024
23 4194304
24 256
25 1048576
26 4096
27 262144
28 4096
29 268435456
30 256
31 1073741824
32 65536
33 1048576
34 65536
35 16777216
36 4096
37 68719476736
38 262144
39 16777216
40 65536
41 1099511627776
42 4096
43 4398046511104
44 1048576
45 16777216
46 4194304
47 70368744177664
48 65536
49 4398046511104
50 1048576
51 4294967296
52 16777216
53 4503599627370496
54 262144
55 1099511627776
56 16777216
57 68719476736
58 268435456
59 288230376151711744
60 65536
61 1152921504606846976
62 1073741824
63 68719476736
64 4294967296
65 281474976710656
66 1048576
67 73786976294838206464
68 4294967296
69 17592186044416
70 16777216
71 1180591620717411303424
72 16777216

Last fiddled with by sweety439 on 2019-11-28 at 08:13
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Old 2019-11-28, 03:29   #30
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Also, assume the conjecture in post https://mersenneforum.org/showpost.p...&postcount=675 is true:

Code:
 n length of largest minimal prime in base n
17 >1000000
19 >707000
21 >506700
25 >660000 (because of the EF{O} family, given by https://github.com/curtisbright/mepn...a/sieve.25.txt)
26 >486700
27 >368000
28 >543000
29 >242300
31 >=524288 (because of the {F}G family, given by https://oeis.org/A275530 and http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt)
32 >=3435973837 (because of the G{0}1 family, given by http://www.prothsearch.com/fermat.html)
33 >10000
34 >10000
35 >10000
36 >32401 (the only two unsolved families are both reserved by me)
37 >=22023 (because of the prime FY{a22021}, given by CRUS)
38 >=16777217 (because of the 1{0}1 family, see http://yves.gallot.pagesperso-orange...s/results.html and http://www.primegrid.com/stats_genefer.php)
39 >10000
40 >25000 (the only one unsolved family is reserved by me)
41 >10000
43 >10000
44 >10000
45 >=18523 (because of the prime O{018521}1, given by CRUS, note that the prime AO{044790}1 is not a minimal prime in base 45, although AO{0}1 is in https://github.com/RaymondDevillers/.../master/left45)
46 >250000 (because of the d4{0}1 family, given by CRUS)
47 >10000
48 >250000 (because of the a{0}1 family, given by CRUS)
49 >=52700 (because of the prime SL{m52698}, given by CRUS)
50 >=16777217 (because of the 1{0}1 family, see http://yves.gallot.pagesperso-orange...s/results.html and http://www.primegrid.com/stats_genefer.php)

Last fiddled with by sweety439 on 2019-11-28 at 08:18
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Old 2019-11-28, 03:49   #31
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Quote:
Originally Posted by sweety439 View Post
Base 36 has only two unsolved family:

(4428*36^n+67)/5
(6480*36^n+821)/7

Base 40 has only two unsolved family:

(13998*40^n+29)/13
(86*40^n+37)/3
The two unsolved family should be:

(559920*40^n+29)/13
(3440*40^n+37)/3

and this (probable) prime should be:

(559920*40^12380+29)/13



(13998*40^12381+29)/13 is the reduced form
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Old 2019-11-29, 06:56   #32
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No (probable) prime found for (86*40^n+37)/3 (S{Q}d in base 40) for n=25K-50K.

Text file attached.

Extended to n=100K.
Attached Files
File Type: txt base 40 S{Q}d family 25K-50K status.txt (37.6 KB, 33 views)
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Old 2019-11-30, 05:51   #33
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Base 36:

O{L}Z (4428*36^n+67)/5: tested to n=50K, no (probable) prime found
{P}SZ (6480*36^n+821)/7: currently at n=41566, no (probable) prime found

Base 40:

S{Q}d (86*40^n+37)/3: currently at n=59777, no (probable) prime found
Attached Files
File Type: txt base 36 O{L}Z family 8K-50K status.txt (151.0 KB, 30 views)
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