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Forum: sweety439 2022-12-01, 15:39
Replies: 385
Views: 60,794
Posted By sweety439
The smallest prime of the form {1}2 in base b...

The smallest prime of the form {1}2 in base b (let the length of this prime be n) is minimal prime (start with b+1) in base b if and only if the length of the smallest prime of the form {1} in base b...
Forum: And now for something completely different 2022-11-28, 19:11
Replies: 202
Views: 44,166
Posted By sweety439
OK, also you can see https://oeis.org/A092559,...

OK, also you can see https://oeis.org/A092559, current the larger prime factor of 2^A092559(n)+1 have been proven prime for all a(n) up to a(52) = 117239, why you skip a(53) = 120788 and prove a(54)...
Forum: And now for something completely different 2022-11-28, 19:04
Replies: 202
Views: 44,166
Posted By sweety439
Primo seems to have a limit of 160000 bits

Primo seems to have a limit of 160000 bits
Forum: Cunningham Tables 2022-11-27, 17:31
Replies: 66
Views: 23,762
Posted By sweety439
Do you mean 2,2222L?

Do you mean 2,2222L?
Forum: sweety439 2022-11-27, 14:03
Replies: 21
Views: 1,613
Posted By sweety439
this number...

this number (http://factordb.com/index.php?id=1100000003974114544) is the 133549th minimal prime (https://primes.utm.edu/glossary/xpage/MinimalPrime.html) in base 25 if we only consider the primes >...
Forum: And now for something completely different 2022-11-27, 13:12
Replies: 84
Views: 12,197
Posted By sweety439
I have an idea for a sequence for prime k-tuples,...

I have an idea for a sequence for prime k-tuples, see https://pzktupel.de/smarchive.php, this sequence seems not to be in OEIS

Smallest k such that there exists all kinds of prime n-tuples <= k
...
Forum: Lounge 2022-11-24, 07:01
Replies: 39
Views: 1,493
Posted By sweety439
Now, I have a prediction .... the game that...

Now, I have a prediction ....

the game that South Korea v.s Uruguay on 2022/11/24 16:00

South Korea = 5128*22^n+1
Uruguay = 3656*22^n-1

Which team wins = Which form requires smaller n to be...
Forum: Lounge 2022-11-24, 06:40
Replies: 39
Views: 1,493
Posted By sweety439
Argentina = 55459*2^n+1 (higher weight) Saudi...

Argentina = 55459*2^n+1 (higher weight)
Saudi Arabia = 10223*2^n+1 (lower weight)

Everyone guess that Argentina should win (55459*2^n+1 should require smaller n to be prime), but the fact is that...
Forum: sweety439 2022-11-24, 06:33
Replies: 21
Views: 1,613
Posted By sweety439
Since 2,1091+ is C307, and it has been sieved...

Since 2,1091+ is C307, and it has been sieved many days with no result (as long as 7,889M), I think that it may be the worst case (i.e. P154*P154), and if so, then it will broke 7,889M's P151 record...
Forum: Cunningham Tables 2022-11-22, 10:26
Replies: 42
Views: 4,340
Posted By sweety439
Are there any numbers with > 229 digits ever been...

Are there any numbers with > 229 digits ever been factored with GNFS (a challenge, factor the 230-digit composite cofactor of R383 with GNFS)? If not, then this 221-digit cofactor of 2,2246M...
Forum: Cunningham Tables 2022-11-22, 10:22
Replies: 42
Views: 4,340
Posted By sweety439
See...

See https://homes.cerias.purdue.edu/~ssw/cun/appc722.txt, you can consider 3,715-, 2,2874M, 10,710M, 7,419- (just a suggestion)
Forum: sweety439 2022-11-22, 04:40
Replies: 385
Views: 60,794
Posted By sweety439
See...

See https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/README.md for more information of this project, including the condensed table (currently the condensed table is...
Forum: sweety439 2022-11-21, 12:31
Replies: 385
Views: 60,794
Posted By sweety439
Records for number of minimal primes (starting...

Records for number of minimal primes (starting with b+1) base b:

2 (1), 3 (3), 4 (5), 5 (22), 7 (71), 8 (75), 9 (151), 11 (1068), 13 (3196 or 3197, 3197 assuming the heuristic argument that all...
Forum: sweety439 2022-11-20, 04:06
Replies: 21
Views: 1,613
Posted By sweety439
This number is very important, since this is the...

This number is very important, since this is the last number 2^n+-1 with n <= the smallest Wieferich prime (1093), thus when this number is fully factored, all 2^n+-1 with n <= the smallest Wieferich...
Forum: Msieve 2022-11-20, 03:57
Replies: 6
Views: 458
Posted By sweety439
This number has as long as 261 digits (and is a...

This number has as long as 261 digits (and is a cofactor of 2^1274-958, which may have SNFS polynomial, but I am not sure), if this number can be factored, then 2^1217-1 (with a composite of 248...
Forum: FactorDB 2022-11-18, 10:15
Replies: 37
Views: 3,546
Posted By sweety439
Well, see...

Well, see https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/tree/main/primality-certificates, these are the primality certificate of these primes, for the unproven PRP see...
Forum: Software 2022-11-18, 10:13
Replies: 788
Views: 125,576
Posted By sweety439
@rogue: Why when click "download" in the...

@rogue:

Why when click "download" in the page https://sourceforge.net/projects/mtsieve/, it only has "srsieve2cl.exe"? It seems that we should click...
Forum: sweety439 2022-11-16, 11:17
Replies: 385
Views: 60,794
Posted By sweety439
https://mersenneforum.org/showpost.php?p=452132&po...

https://mersenneforum.org/showpost.php?p=452132&postcount=66

The numbers in x{y}z (where x and z are strings (may be empty) of digits in base b, y is a digit in base b) families are of the form...
Forum: sweety439 2022-11-16, 10:56
Replies: 385
Views: 60,794
Posted By sweety439
For the numbers < 10^25000, I require them to be...

For the numbers < 10^25000, I require them to be definitely primes (i.e. not merely probable primes), N-1 proving (https://primes.utm.edu/prove/prove3_1.html) or N+1 proving...
Forum: FactorDB 2022-11-14, 00:39
Replies: 37
Views: 3,546
Posted By sweety439
Well .... I hope that there is a "Minimal primes:...

Well .... I hope that there is a "Minimal primes: ECPP proofs" thread, like the "Leyland Primes: ECPP proofs" thread (https://mersenneforum.org/showthread.php?t=19348), for both of them (the large...
Forum: sweety439 2022-11-14, 00:19
Replies: 385
Views: 60,794
Posted By sweety439
New link for GitHub:...

New link for GitHub: https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers (I renamed it, I think that this name is better)
Forum: Riesel Prime Search 2022-11-13, 05:15
Replies: 103
Views: 48,471
Posted By sweety439
Why k must be > 4? I know that for even k the...

Why k must be > 4? I know that for even k the form can be reduced to k' = k/2, but what about k = 1 and k = 3?

Also, are there sieve files for k*2^n+1 as well as k*2^n-1?
Forum: sweety439 2022-11-12, 00:25
Replies: 3
Views: 470
Posted By sweety439
Also, outside number theory, 24 is also very...

Also, outside number theory, 24 is also very important because ....

* 24 is the largest n such that 1^2+2^2+3^2+4^2+...+n^2 is square.
* 24 is the Euler characteristic of a K3 surface.
* The...
Forum: sweety439 2022-11-10, 19:19
Replies: 1
Views: 311
Posted By sweety439
Extend many classic problems to bases 2 <= b <= 36

1. Lychrel number (https://en.wikipedia.org/wiki/Lychrel_number) (function "N + reverse of N" until reach a palindrome, e.g. 78 + 87 = 165, 165 + 561 = 726, 726 + 627 = 1353, 1353 + 3531 = 4884 and...
Forum: sweety439 2022-11-08, 12:59
Replies: 21
Views: 1,613
Posted By sweety439
Its termination is unusual, terminate at a...

Its termination is unusual, terminate at a relative larger prime 347, most terminations of a number which reaches to 100 digits or more are a prime < 100
Showing results 1 to 25 of 1000

 
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