20190627, 10:11  #23 
Banned
"Luigi"
Aug 2002
Team Italia
3·1,619 Posts 

20190627, 13:36  #24 
Mar 2019
2·163 Posts 
Perhaps the author of mmff could comment on the feasibility of modifying this program to find Double Wagstaff factors, and if so, how it would need to be changed?

20190627, 15:06  #25  
Sep 2003
3·863 Posts 
Quote:
It is not nearly as simple as the changes that were made to mfaktc to handle Wagstaff, which was a mere handful of #ifdef statements. The mfaktc code can handle any arbitrary exponent up to a certain limit, including MM31 (exponent = about 2.1 billion), but not the huge "double" exponents. I used it to test WW31 (exponent = about 715 million) up to TF=2^80 and found one small factor of about 62 bits. WW43 (exponent = about 2.9 trillion) is out of reach. The Double Mersenne search hasn't had any results beyond MM31. The most recent of four factors of MM31 was found in 2005, so probably mmff was not used to find it. Since Double Mersenne hasn't had much success and seems to have only two currently active users, and Wagstaff has much less overall interest than Mersenne, and creating Double Wagstaff code would involve nontrivial specialized effort, it's kind of hard to make a case for doing Double Wagstaff. 

20191115, 04:55  #26 
"Dylan"
Mar 2017
1122_{8} Posts 
I don't know if there has been any update to searching for factors of double Wagstaffs, but I searched for potential factors of W(W(42737)), using pfgw64 with the f1 flag, and the following input:
Code:
ABC2 2*$a*((2^42737+1)/3)+1 a: from 1 to 50000 Code:
2*21085*((2^42737+1)/3)+1 2*42289*((2^42737+1)/3)+1 Although this is reasonably quick (a test takes about half a second), there's a lot of candidates with a factor of 3, so a sieve would be good for a serious search. 
20191115, 06:11  #27 
Jun 2003
1010100111011_{2} Posts 
Wagstaff factors must be 1 or 3 (mod 8). Your numbers are 7 (mod 8). So they can't divide.
But if you want to test them, you can use Pari/GP Code:
? W=(2^42737+1)/3; ? N=2*21085*((2^42737+1)/3)+1; ? Mod(2,N)^W+1 == 0 %1 = 0 Last fiddled with by axn on 20191115 at 06:19 
20191117, 21:12  #28 
"Dylan"
Mar 2017
2×3^{3}×11 Posts 
Thanks axn for the advice. I've updated the ABC2 header:
Code:
ABC2 2*(4*$a)*((2^42737+1)/3)+1  2*(4*$a+3)*((2^42737+1)/3)+1 a: from 0 to 62500 Code:
2*(4*13918+3)*((2^42737+1)/3)+1 2*(4*18327+3)*((2^42737+1)/3)+1 2*(4*26962+3)*((2^42737+1)/3)+1 2*(4*34111)*((2^42737+1)/3)+1 2*(4*38520)*((2^42737+1)/3)+1 2*(4*45025)*((2^42737+1)/3)+1 2*(4*54945)*((2^42737+1)/3)+1 2*(4*58207)*((2^42737+1)/3)+1 2*(4*58308+3)*((2^42737+1)/3)+1 
20191118, 02:49  #29 
Jun 2003
153B_{16} Posts 
I did a search of all k < 10^6. Here are the primes. No factors, natch.
Code:
2*55675*((2^42737+1)/3)+1 2*73311*((2^42737+1)/3)+1 2*107851*((2^42737+1)/3)+1 2*136444*((2^42737+1)/3)+1 2*154080*((2^42737+1)/3)+1 2*180100*((2^42737+1)/3)+1 2*219780*((2^42737+1)/3)+1 2*232828*((2^42737+1)/3)+1 2*233235*((2^42737+1)/3)+1 2*266260*((2^42737+1)/3)+1 2*284271*((2^42737+1)/3)+1 2*308163*((2^42737+1)/3)+1 2*319195*((2^42737+1)/3)+1 2*340684*((2^42737+1)/3)+1 2*341500*((2^42737+1)/3)+1 2*348316*((2^42737+1)/3)+1 2*367168*((2^42737+1)/3)+1 2*368020*((2^42737+1)/3)+1 2*406035*((2^42737+1)/3)+1 2*427771*((2^42737+1)/3)+1 2*464971*((2^42737+1)/3)+1 2*468720*((2^42737+1)/3)+1 2*470836*((2^42737+1)/3)+1 2*534735*((2^42737+1)/3)+1 2*535951*((2^42737+1)/3)+1 2*574444*((2^42737+1)/3)+1 2*576928*((2^42737+1)/3)+1 2*580056*((2^42737+1)/3)+1 2*623875*((2^42737+1)/3)+1 2*628611*((2^42737+1)/3)+1 2*639783*((2^42737+1)/3)+1 2*652996*((2^42737+1)/3)+1 2*691695*((2^42737+1)/3)+1 2*759304*((2^42737+1)/3)+1 2*771864*((2^42737+1)/3)+1 2*795195*((2^42737+1)/3)+1 2*813655*((2^42737+1)/3)+1 2*823683*((2^42737+1)/3)+1 2*902104*((2^42737+1)/3)+1 2*925608*((2^42737+1)/3)+1 2*953796*((2^42737+1)/3)+1 2*995536*((2^42737+1)/3)+1 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Status of Wagstaff testing? and testing Mersenne primes for Wagstaffness  GP2  Wagstaff PRP Search  414  20201227 08:11 
Large gaps between Wagstaff prime exponents  Bobby Jacobs  Wagstaff PRP Search  2  20190303 19:37 
Statistical odds for prime in Wagstaff vs Mersenne  diep  Math  27  20100113 20:18 
30th Wagstaff prime  T.Rex  Math  0  20070904 07:10 
Silverman & Wagstaff on Joint Distribution of Ultimate and Penultimate Prime Factors  wblipp  Math  12  20060402 18:40 