20190604, 16:27  #221 
Aug 2006
2^{2}·5·293 Posts 

20190604, 17:08  #222  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{8}·3·5 Posts 
Quote:
http://www.hoegge.dk/mersenne/NMC.html has entries for M82589933, M268435459, M1073741827, M2147483647; some rather long gaps there. Maybe add ~134M and ~537M. M1073741827 would take nearly 2 years to PRP test on an NVIDIA GTX 1080 Ti in gpuowl v6.5. That's a lot of gpu throughput to invest in one more data point for what RDS calls basically a joke. 

20190604, 18:19  #223 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
2×3×5×7×43 Posts 

20190604, 18:28  #224 
Bamboozled!
May 2003
Down not across
3^{2}×11×101 Posts 

20190604, 19:05  #225  
Sep 2003
2×1,289 Posts 
Quote:
Until new Mersenne primes are discovered, the only exponents that could possibly refute the conjecture in our lifetimes are 1,073,741,827 = 4**15+3 and 2,147,483,647 = 2**31−1 (aka MM31). The latter already has known factors (as a Mersenne number, not as a Wagstaff number). After that the next possible exponent is 2**61−1 (aka MM61), which is utterly infeasible. I'm not sure what your "~134M and ~537M" refer to. It's hardly a priority, but on the other hand someone actually completed an LL test of M999,999,937 for no particular reason. And this number has only 7.37% more digits. If anyone has an appetite for more senselessly large exponents, might as well do that one. 

20190604, 20:17  #226 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
111100000000_{2} Posts 
p near 2^{27} and 2^{29}. But that would require prime p's in the right places. And they're not there.
k=27, 2^k:134,217,728 +1= 3^4 × 19 × 87211 1= 7 × 73 × 262657 4^k not applicable k=29, 2^k: 536,870,912 +1= 3 × 59 × 3 033169 1= 233 × 1103 × 2089 So we keep hunting for Mersenne primes. Last fiddled with by kriesel on 20190604 at 20:21 
20190604, 21:08  #227  
Sep 2003
A12_{16} Posts 
Quote:
Thus it is almost certainly trivially true. Last fiddled with by GP2 on 20190628 at 15:20 Reason: a factor was discovered for M1,073,741,827 

20190610, 20:14  #228  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{8}×3×5 Posts 
Quote:
mersenne.ca shows M1073741827 TF is done to 82 bits (vs. GPU72 goal 86), and M2147483647 done up to 86 bits (vs. GPU72 goal 89), with 4 factors already found. I'm not aware of any software available suitable for reasonable speed P1 factoring attempts on these 3. Nor primality testing software for reasonable speed PRP testing of these, except gpuowl for M1073741827. 

20190610, 20:50  #229  
Sep 2003
2·1,289 Posts 
Quote:
mfaktc can factor Wagstaff numbers if you edit the params.h file to uncomment the #define WAGSTAFF line and recompile everything. If you do that, it's best to rename the executable to something like "wfaktc.exe" so you don't accidentally use it on Mersennes. 

20190610, 21:46  #230  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{8}×3×5 Posts 
Quote:
Quote:
Have you tackled any Wagstaff TF above W2147483647? (Mfaktx and variants are I think limited to 2^32 exponent.) 

20190610, 23:06  #231  
Sep 2003
2·1,289 Posts 
Quote:
If I recall, doing TF to 82 bits for these exponents on a Tesla V100 took maybe one or two days. If I had fulltime use of one of the new fast GPUs, I'd take them to 86 bits myself. 

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