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
3×7×167 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
9687_{10} 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
"name field"
Jun 2011
Thailand
2684_{16} 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
2^{2}×3×17×31 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
20300_{8} 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
6324_{10} Posts 

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