20120923, 21:51  #12 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 

20120924, 01:47  #13  
"Jason Goatcher"
Mar 2005
3·7·167 Posts 
Quote:
I ask because some people say they're 100% certain about something when it's actually only a strong opinion. Not making any sort of accusation, just asking for clarification. 

20120924, 02:19  #14  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:


20120924, 02:34  #15  
"Jason Goatcher"
Mar 2005
3507_{10} Posts 
Quote:
2*1*M43112609+1 Typed it out for anyone that's as slow as I am :) 

20120924, 02:43  #16  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Quote:
Finally, from the math page, it requires O(p) squarings mod q to test if q divides 2^p1; given the absolutely gargantuan values of p and q, I'm relatively sure that no one has tried (it would take about as much work, asymptotically speaking, to test 2^p1%q as to test p for primality with the LL test). 

20120924, 05:17  #17  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2558_{16} Posts 
Quote:
2*2*M43112609+1 is divisible by 5. ... k>=5 dude. (Common knowledge for MMp.) Sieve a little bit, then do what KEP did; maybe one of you will get lucky! Last fiddled with by Batalov on 20120924 at 05:23 

20120924, 06:56  #18 
Romulan Interpreter
Jun 2011
Thailand
5^{2}×17×23 Posts 
In fact, as Mp is 3 mod 4, when looking for factors of MMp of the form q=2*k*Mp+1, we are interested only in k=0,1 (mod 4). So, k can only be 1,4,5,8,9,12,13,16,17, etc.
But as Batalov pointed, for k=1 (therefore 1,4,7,10,13,etc) all q's are 0 mod 3, because Mp is 1 mod 3. Same for mod 5, Mp=1, so k=2,7,12,17,22,27,32,etc are all excluded. Mp=3 (mod 7) so for all k=1,8,15,22,29, etc results in q's being 0 mod 7. etc etc Intersecting all this stuff, the most k's are gone very fast. Using primes below 1M, very few k remain. k=5 will be gone if we extend higher, 2*5*Mp+1 is divisible with 582994261. Next k which does not... succumb under the filter with small primes is k=185 (tested with primes under 1G4), and behind of it, k=201. So, if someone can prove that 2*185*Mp+1 is prime, be my guest 
20120924, 07:22  #19 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3×7×13×23 Posts 
Oh, this one is easy to prove prime using the "Terrence Law" method. No small factors have been found, so 2*185*M43112609+1 is prime
What do I win? 
20120924, 12:23  #20  
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
Quote:
Last fiddled with by science_man_88 on 20120924 at 12:24 

20120924, 13:18  #21 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Mp mod 2 to 1000
Code:
1,1,3,1,1,3,7,4,1,5,7,5,3,1,15,1,13,9,11,10,5,1,7,11,5,13,3,1,1,15,31,16,1,31,31,17,9,31,31,19,31,1,27,31,1,16,31,10,11,1,31,30,13,16,31,28,1,30,31,29,15,31,63,31,49,6,35,1,31,9,31,36,17,61,47,38, 31,8,31,67,19,78,31,1,1,1,71,1,31,31,47,46,63,66,31,24,59,49,11,6,1,6,31,31,83,62,67,53,71,91,31,1,85,1,59,31,89,52,31,5,29,19,15,11,31,1,127,1,31,87,115,66,73,121,103,119,1,91,31,16,9,5,31,1,109,10,91, 49,61,75,47,103,115,46,31,28,87,136,31,24,67,147,19,16,161,3,31,70,1,85,87,96,1,136,159,148,1,57,31,89,31,151,47,91,139,137,63,94,161,2,127,167,121,31,59,158,49,150,111,73,107,59,103,101,109,139,31, 104,31,190,83,151,169,1,175,108,53,109,71,18,91,33,31,211,1,196,199,176,1,115,175,75,31,16,207,166,171,71,31,208,5,67,151,206,19,161,15,244,11,9,31,93,1,1,255,1,1,17,31,175,87,203,247,136,199,1,207, 155,121,120,239,31,119,236,139,37,91,139,31,179,157,57,151,256,5,101,31,35,1,121,255,113,157,266,239,148,49,70,211,87,75,208,47,151,103,193,115,109,201,62,31,288,185,31,87,124,295,291,191,169,185, 256,67,161,147,271,183,157,181,165,327,202,3,6,31,255,239,1,171,170,85,255,87,1,269,163,175,49,311,148,159,1,325,151,179,52,57,218,31,142,89,247,31,36,151,31,47,265,91,136,139,213,137,136,63,291, 283,122,351,1,193,27,127,346,167,130,315,33,31,1,255,349,355,166,247,1,349,199,111,110,73,356,107,391,59,313,103,159,101,256,315,325,139,161,31,91,313,97,31,344,401,157,295,86,151,395,383,148,1, 297,175,305,325,1,271,47,109,55,71,157,239,401,91,1,33,49,255,1,211,60,227,226,423,31,199,422,405,256,231,453,115,41,175,46,75,223,31,73,251,28,207,302,403,161,171,454,71,137,31,239,449,346,247, 121,67,268,151,310,451,118,19,1,161,346,15,80,493,494,11,337,9,91,31,6,93,70,255,202,1,255,511,256,1,6,259,16,17,442,31,369,175,247,87,136,203,511,511,323,401,148,199,265,1,276,207,415,155,500, 391,64,391,451,511,271,31,477,119,517,511,465,415,87,37,91,91,22,139,44,31,511,179,294,439,1,57,472,151,281,541,488,291,193,101,461,319,92,35,553,291,493,121,401,255,31,113,7,451,294,561,355,239, 123,445,171,347,349,369,341,511,511,87,274,75,126,511,141,351,262,151,486,103,192,193,511,423,1,109,614,511,553,373,535,31,11,601,313,499,239,31,315,87,190,441,1,295,304,291,364,511,638,169,632, 507,1,579,24,391,148,161,325,147,423,271,611,511,328,157,532,511,550,165,460,327,66,535,1,3,256,341,456,31,509,255,661,239,173,1,24,511,196,511,1,427,256,255,634,431,83,1,534,615,346,163,91,175, 511,49,541,311,498,499,313,511,16,1,612,679,78,151,166,535,139,409,291,415,310,577,168,31,521,503,208,451,436,247,452,31,67,401,1,151,31,31,451,415,676,265,734,91,655,507,172,511,496,213,742, 511,276,511,433,63,511,291,226,283,318,501,346,351,367,1,598,575,256,27,148,511,606,731,1,167,362,517,511,703,535,33,142,31,577,1,175,255,656,349,270,355,466,561,227,247,395,1,136,747,289,199, 392,511,535,511,401,475,346,759,424,511,637,391,64,59,391,313,636,511,560,159,31,511,491,667,651,727,511,325,469,139,34,161,37,447,647,91,671,731,418,97,285,31,581,765,460,823,746,157,731, 719,340,511,461,151,274,395,256,383,742,577,308,431,388,297,817,607,96,305,613,759,324,1,408,271,121,47,136,547,141,55,406,511,44,157,626,239,856,401,333,535,255,1,148,479,674,49,236,255,70, 1,697,211,613,511,388,679,451,679,72,423,814,31,241,655,742,879,151,863,87,715,102,231,193,453,577,115,461,41,418,639,112,511,598,75,373,223,511,31,782,73,601,251,362,499,921,207,661,775,283, 403,109,161,124,647,833,931,766,71,610,137,941,511,418,239,490,931,746,829,247,247,256,121,741,67,647,755,811,639,944,799,357,451,598,609,468,511,946,1,157,655,1,841,24,511,496,577,946,991, 352,993,202,511, Last fiddled with by science_man_88 on 20120924 at 13:53 
20120924, 13:35  #22 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3×7×13×23 Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is CEMPLLA 1.5 "the only software in the world capable of discovering" something? Not really.  CRGreathouse  Number Theory Discussion Group  51  20181216 21:55 
Official "World cup 2014/2018" teat  LaurV  Hobbies  74  20180711 19:33 
Problem E7 of Richard Guy's "Unsolved problems in number theory"  Batalov  Computer Science & Computational Number Theory  40  20130316 09:19 
Is the USA the "new" peacekeeper of the world??  outlnder  Soap Box  20  20050203 09:30 
Would Minimizing "iterations between results file" may reveal "is not prime" earlier?  nitai1999  Software  7  20040826 18:12 