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Forum: sweety439 2021-01-14, 19:17
Replies: 136
Views: 6,312
Posted By sweety439
For more lengths for the smallest prime of the...

For more lengths for the smallest prime of the form k*b^n+1 (form: k{0}1) or k*b^n-1 (form: x{y}, x = k-1, y = b-1) with k<b in base b, see CRUS (http://www.noprimeleftbehind.net/crus/)

Note: This...
Forum: sweety439 2021-01-14, 04:55
Replies: 136
Views: 6,312
Posted By sweety439
Large minimal prime (start with b+1) for bases...

Large minimal prime (start with b+1) for bases b>16 not in the list for bases 2 to 30 (https://github.com/curtisbright/mepn-data/tree/master/data) or list for bases 28 to 50...
Forum: sweety439 2021-01-14, 04:50
Replies: 136
Views: 6,312
Posted By sweety439
Length of largest minimal prime (start with b+1)...

Length of largest minimal prime (start with b+1) in base b for b = 2, 3, 4, ..., 40:

2, 3, 3, 96, 5, >=17, 221, >=1161, 31, >=45, 42, >=32021, >=19699, >=107, >=32235, >=111334, >=300, >=110986,...
Forum: sweety439 2021-01-14, 03:53
Replies: 136
Views: 6,312
Posted By sweety439
Found another minimal prime (start with b+1) in...

Found another minimal prime (start with b+1) in base b=14:

1879B

Found three other minimal primes (start with b+1) in base b=15:

33301431
6330261
605331
Forum: sweety439 2021-01-14, 01:21
Replies: 136
Views: 6,312
Posted By sweety439
Update newest data file.

Update newest data file.
Forum: sweety439 2021-01-13, 16:48
Replies: 136
Views: 6,312
Posted By sweety439
Update newest pdf file. Minimal elements for...

Update newest pdf file.

Minimal elements for the base b representations of the primes which are > b...
Forum: sweety439 2021-01-13, 15:57
Replies: 136
Views: 6,312
Posted By sweety439
DB32234 (base 16) is probable prime!!! This...

DB32234 (base 16) is probable prime!!!

This number is like the largest minimal prime (start with 2 digits) in base 16

The families 5{7} (base 11) and 9{5} (base 13) still no (probable) prime...
Forum: sweety439 2021-01-12, 19:09
Replies: 136
Views: 6,312
Posted By sweety439
The b^n-2 case should require n>1, since...

The b^n-2 case should require n>1, since single-digit primes are not acceptable in this puzzle, thus the smallest primes should be:

7, 23, 47, 79, 14639, 167, 223, 24137567, 359, 439,...
Forum: sweety439 2021-01-12, 19:03
Replies: 136
Views: 6,312
Posted By sweety439
This puzzle is an extension of the original...

This puzzle is an extension of the original minimal prime base b puzzle (https://www.primepuzzles.net/puzzles/puzz_178.htm), to include CRUS Sierpinski...
Forum: sweety439 2021-01-12, 18:59
Replies: 136
Views: 6,312
Posted By sweety439
The corresponding families: * repunit prime...

The corresponding families:

* repunit prime base b: {1}
* generalized Fermat prime base b for even b: 1{0}1
* generalized half Fermat prime (> (b+1)/2) base b for odd b: {x}y, x = (b-1)/2, y =...
Forum: sweety439 2021-01-12, 18:50
Replies: 136
Views: 6,312
Posted By sweety439
* The smallest prime of the form 2*b^n+1 (for b...

* The smallest prime of the form 2*b^n+1 (for b != 1 mod 3): [not minimal prime (start with 2 digits) if b<=2]

5, 7, 11, 13, 17, 19, 23, 3457, 29, 31,...
Forum: sweety439 2021-01-10, 22:21
Replies: 136
Views: 6,312
Posted By sweety439
fixed typo in the file: 3*16^n+1 should be...

fixed typo in the file: 3*16^n+1 should be 3*4^n+1, 12^((n+1)/2) +/- 5 should be 12^((n+2)/2) +/- 5
Forum: sweety439 2021-01-10, 20:09
Replies: 136
Views: 6,312
Posted By sweety439
All known minimal primes (start with b+1) in...

All known minimal primes (start with b+1) in bases 2<=b<=16: (data for bases 2, 3, 4, 5, 6, 8, 10, 12 are known to be complete)

Also three unsolved families are known:

Base 11: 5777...777
Base...
Forum: sweety439 2021-01-10, 19:28
Replies: 136
Views: 6,312
Posted By sweety439
There are totally 106 minimal primes (start with...

There are totally 106 minimal primes (start with 2 digits) in base 12, there are 77 such primes in base 10
Forum: sweety439 2021-01-10, 19:27
Replies: 136
Views: 6,312
Posted By sweety439
Now, we proved the set of minimal primes (start...

Now, we proved the set of minimal primes (start with b+1, which is equivalent to start with b, if b is composite) of base b=12:


11
15
17
1B
25
27
31
Forum: sweety439 2021-01-10, 12:09
Replies: 136
Views: 6,312
Posted By sweety439
I have made a pdf file about this project, see...

I have made a pdf file about this project, see the attached file in post #114 (https://mersenneforum.org/showpost.php?p=568813&postcount=114)

Well, the proofs for base 2, 3, 4 are really trivial,...
Forum: sweety439 2021-01-09, 21:18
Replies: 136
Views: 6,312
Posted By sweety439
Now I am reserving these families, currently at...

Now I am reserving these families, currently at about length 15000, still no (probable) primes found

Base 11: 5{7}
Base 13: 9{5}
Base 16: D{B}
Forum: sweety439 2021-01-09, 19:11
Replies: 34
Views: 1,543
Posted By sweety439
https://members.loria.fr/PZimmermann/records/ ...

https://members.loria.fr/PZimmermann/records/

https://members.loria.fr/PZimmermann/records/Wieferich.status
Forum: sweety439 2021-01-09, 19:11
Replies: 34
Views: 1,543
Posted By sweety439
I create this thread, the target is collect links...

I create this thread, the target is collect links of primes to offer people to click, some of the links are difficult to find
Forum: sweety439 2021-01-09, 17:08
Replies: 115
Views: 9,454
Posted By sweety439
Update status files in base 36

Update status files in base 36
Forum: sweety439 2021-01-09, 13:31
Replies: 34
Views: 1,543
Posted By sweety439
https://primes.utm.edu/ ...

https://primes.utm.edu/
https://primes.utm.edu/primes/
https://primes.utm.edu/notes/faq/
https://primes.utm.edu/top20/home.php
https://primes.utm.edu/prove/index.html...
Forum: sweety439 2021-01-09, 10:53
Replies: 136
Views: 6,312
Posted By sweety439
Found a large minimal prime (start with 2 digits)...

Found a large minimal prime (start with 2 digits) in base 9: 30115811, which equals 3*9^1160+10
Forum: sweety439 2021-01-09, 10:38
Replies: 136
Views: 6,312
Posted By sweety439
No, I was proving the set of the minimal elements...

No, I was proving the set of the minimal elements of the prime strings with length >=2 in bases 8, 10, 12, with step-by-step instructions, e.g. for base 8, I was proving the case that (first...
Forum: sweety439 2021-01-09, 10:34
Replies: 136
Views: 6,312
Posted By sweety439
I have a pdf file for the proof (not complete,...

I have a pdf file for the proof (not complete, continue updating), I will complete the proof for bases 7, 9, 12
Forum: sweety439 2021-01-09, 10:23
Replies: 34
Views: 1,543
Posted By sweety439
primes of the form k*2^n+1:...

primes of the form k*2^n+1: http://www.prothsearch.com/

primes of the form k*2^n-1: http://www.15k.org/
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