20170406, 17:30  #12  
Sep 2002
Database er0rr
2·3·23·31 Posts 
Quote:


20170406, 17:32  #13  
"Forget I exist"
Jul 2009
Dumbassville
20CF_{16} Posts 
Quote:


20170406, 22:13  #14  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,967 Posts 
Quote:
Quote:
...But you don't know how long that calculation took (and only for that single value). But you can know: just find the next value n > 10000076282 so that p(n) is PRP. Or the previous n (i.e. slightly below 10^10). And the same question: what is n :: A046063(n) = 10000076282 ? 

20170407, 00:47  #15  
Sep 2002
Database er0rr
2·3·23·31 Posts 
Quote:
Edit: I am revising my guess to 62 hours, based on: Code:
time echo "numbpart(10^10/2^8);"  gp q real 0m8.736s user 0m8.468s sys 0m0.016s time echo "numbpart(10^10/2^7);"  gp q real 0m29.226s user 0m28.488s sys 0m0.016s time echo "numbpart(10^10/2^6);"  gp q real 1m41.768s user 1m41.884s sys 0m0.020s ? 28.488/8.468 3.3641946150212564950401511572980632971 ? 101.884/28.488 3.5763830384723392305532153889356922213 ? (3.6)^6*102/3600 61.675499520000000000000000000000000000 Last fiddled with by paulunderwood on 20170407 at 01:24 

20170418, 16:15  #16 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9934_{10} Posts 

20170420, 22:55  #17 
Sep 2002
Database er0rr
2·3·23·31 Posts 

20170421, 18:36  #18  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,967 Posts 
Quote:
To revise my own estimate I ran a small search for an even larger PRP p(n), n > 14180076200 (a randomly chosen starting point*). It took ~10 hrs x 80 threads, so it is not a very trivial computation. The new largest known PRP is p(14180123587),which has 132646 decimal digits. _________________ *Note that the decimal size of p(n) is known to be ~ \(1.114 \sqrt n\) (due to Hardy and Ramanujan, 1918) 

20170421, 19:10  #19  
Sep 2002
Database er0rr
10266_{8} Posts 
Quote:


20170426, 19:58  #20 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,967 Posts 
A couple of larger PRPs was also found, the larger slightly above 200000 decimal digits.
numbpart(32235776596), 200002 digit size 
20170426, 20:06  #21  
Sep 2002
Database er0rr
10B6_{16} Posts 
Quote:
How long does it take ARB to generate such a number? Last fiddled with by paulunderwood on 20170426 at 20:09 

20170426, 20:53  #22 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,967 Posts 
Only 0.85s to generate number.
~13 minutes to check with PFGW. In this size range you would expect to need to check 460000 candidates (of which you can sieve away 9598%, but you'd still need to run a few thousand PRP tests). So the estimate is ~10^3 cpuhours to find one. 
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