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
6663_{8} 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
3×7×479 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
3·23·149 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
2·3,343 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
Dartmouth NS
2·3·23·61 Posts 
Quote:
Last fiddled with by science_man_88 on 20120924 at 12:24 

20120924, 13:18  #21 
"Forget I exist"
Jul 2009
Dartmouth NS
2·3·23·61 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
1A1E_{16} Posts 

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