Thread for posting tiny primes

[CRGreathouse]

Originally Posted by science_man_88

it's my birthday I would show the birthday rhyme of happy birthday i made but it's not going to get any laughs.

Happy birthday.

[3.14159]

Two #6 entries for Karsten. Accepted.

[3.14159]

Looking for 28900-digit and 33866-digit primes.

The former is k * 4489!^2 + 1, the latter being k * 2^112480 + 1, along with the main search; k * 2^594800 + 1.

[kar_bon]

PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing 1177*40009#+1 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 100.00% and helper 0.01% (300.01% proof)
1177*40009#+1 is prime! (903.9856s+0.0199s)

17280 digits

[axn]

Originally Posted by kar_bon

PFGW Version 3.3.6.20100908.Win_Stable [GWNUM 25.14]
Primality testing 1177*40009#+1 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 100.00% and helper 0.01% (300.01% proof)
1177*40009#+1 is prime! (903.9856s+0.0199s)

17280 digits

Are you using -tc? -tp should be sufficient.

[kar_bon]

Originally Posted by axn

Are you using -tc? -tp should be sufficient.

Yes to be sure, but used -tp also.

[3.14159]

Hmm.. Another #6 by Karsten. Accepted.

I have a #3 entry: 51222 * 4489!^2 + 1 (28900 digits)

Verification:
Primality testing 51222*4489!^2+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 4493
Generic modular reduction using generic reduction FFT length 10K on A 96001-bit number
Running N-1 test using base 4513
Generic modular reduction using generic reduction FFT length 10K on A 96001-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 35.00%
51222*4489!^2+1 is prime! (150.8117s+0.0037s)

Also a #1 entry: 211975 * 2^112480 + 1. (33866 digits)

Verification:
Primality testing 211975*2^112480+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Special modular reduction using zero-padded FFT length 12K on 211975*2^112480+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
211975*2^112480+1 is prime! (24.3142s+0.0007s)

[cmd]

Originally Posted by science_man_88

it's my birthday I would show the birthday rhyme of happy birthday i made but it's not going to get any laughs.

this "base" number to find ... Mn

count the number of legs





( o - f )

[kar_bon]

So Kevin, where is your list and the top 10 of every type?

I don't know which number to beat.

But here's one for factoring a number:

Normally SIQS is for numbers up to about 90 or 100 digits in length, but I wanted to show, it's doable with higher ones.

Note: I know with msieve that result would be much easier and quicker but with SIQS (with yafu) should stand for a long time as a new record so far!

I've done this on a Q6600 with all 4 cores.

For more details see the attachment.

[3.14159]

My list? I'll repost..

The primes that I will search for:

1. Proths, where b is 2.
2. Generalized Proths, where b is any integer.
3. Factorial-based proths, where b is a factorial number.
4. Primorial-based proths, where b is a primorial number.
5. Prime-based proths, where b is a prime number.
6. Primorial, k * p(n) + 1
7. Factorial, k * n! + 1
8. Generalized Cullen/Woodall, k * b^k + 1
9. Factorial Cullen/Woodall, where b, optionally k, is a factorial number.
10. Primorial Cullen/Woodall, where b, optionally k, is a primorial number.
11. Prime-based Cullen/Woodall, where b is a prime number
12. k-b-b, numbers of the form k * b^b + 1
13. Factorial k-b-b, where b, optionally k, is a factorial number.
14. Primorial k-b-b, where b, optionally k, is a primorial number.
15. Prime-based k-b-b, where b is a prime number.
16. Number, square, and fourth, where n^1 + 1, n^2 + 1, and n^4 + 1 are all primes.
17. Special Cofactor, where the prime cofactor is of one of the forms used in this list.
18. General Cofactor, where the prime cofactor is not of a special form.
19. General arithmetic progressions, k * b^n + c, where c is a prime > 10^2, where the prime is at least 2000 digits in length, and where the exponent n > 1.
20. Obsolete-tech-proven primes, using the original PrimeForm or Proth.exe, or any other prime to prove primality of any type of prime listed here. Note: The prime must be at least 7500 digits in length.
21. N-1 analogues of items 1-5.
22. N-1 analogues of items 6 and 7.
23. N-1 analoges of items 8-11.
24. N-1 analogues of items 12-15.
25. Obsolete-tech-proven primes, for -1 analogues only.
26. Twins.

User 3.14159 searches for items 1-20; Other members: 21-26.

[3.14159]

Top 10? I can't remember all the entries made.. Let's just make it the largest 10 primes for any category on the list.

Batalov holds the record at 219561 digits:

(1)4 * 17^178438 + 1 (219561 digits) #2. (Batalov)
(2)912646 * 798336^20160 + 1 (118995 digits) (3.14159/Kevin)
(3)2778 * 211^47085 - 1 (109446 digits) (Mdettweiler/Max)
(4)2336 * 75^43523 + 1 (81612 digits) (Mdettweiler/Max)
(5)22147 * 2^256720 + 1 (77285 digits) (3.14159/Kevin)
(6)3782 * 75^41086 + 1 (77043 digits) (Mdettweiler/Max)
(7)207408 * 77906^8192 + 1 (40078 digits) (3.14159/Kevin)
(8)2093 * 600!^26 + 1 (36614 digits) (3.14159/Kevin)
(9)698046 * 1999^10480 + 1 (34599 digits) (3.14159/Kevin)
(10)211975 * 2^112480 + 1 (33866 digits) (3.14159/Kevin)