20201022, 10:47  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
13·491 Posts 
Primes made mostly of nines
10^10000  10^8668  1 is a pseudoprime; can I assert that it's prime because we've got a very boring factorisation of 86.68% of n+1 ?

20201022, 11:31  #2 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×7^{2}×109 Posts 

20201022, 11:34  #3 
"Oliver"
Sep 2017
Porta Westfalica, DE
494_{10} Posts 
FactorDB instantly proved it by N+1 as being prime.

20201022, 11:58  #4  
"Robert Gerbicz"
Oct 2005
Hungary
2×733 Posts 
Quote:
with F1=1, F2=10^8668. 

20201022, 13:33  #5  
(loop (#_fork))
Feb 2006
Cambridge, England
13×491 Posts 
Quote:
(my housemate had found a tweet getting excited about a 6400digit prime comprised entirely of nines with a single eight, and I thought this was not a particularly exciting result) 

20201022, 13:46  #6  
Sep 2002
Database er0rr
3^{2}×11×37 Posts 
Quote:
Code:
./pfgw64 tp q"10^10000  10^8668  1" T4 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 10^10000  10^8668  1 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 43, base 1+sqrt(43) 10^10000  10^8668  1 is prime! (10.6651s+0.0255s) Back in the day, we found this one when PRP tests took 100 mins each on Athlons at 1GHz. What programs have you been using to find your prime? The following was done on one core of a Haswell at 3.7GHz. Code:
cat NRD_gigantic ABC2 10^1000010^$a1 a: from 1 to 9999 Code:
time ./pfgw64 N f NRD_gigantic PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Recognized ABC Sieve file: ABC2 File ***WARNING! file NRD_gigantic may have already been fully processed. 10^1000010^7501 has factors: 2313617 10^1000010^15891 has factors: 2635553 10^1000010^34861 is 3PRP! (1.1229s+0.0885s) 10^1000010^39091 is 3PRP! (1.0102s+0.1867s) 10^1000010^41511 has factors: 376769 10^1000010^51331 is 3PRP! (1.0614s+0.0897s) 10^1000010^53341 has factors: 772147 10^1000010^61341 has factors: 2749921 10^1000010^79281 is 3PRP! (1.1574s+0.1369s) 10^1000010^80721 has factors: 2742227 10^1000010^86681 is 3PRP! (0.9757s+0.0931s) 10^1000010^87401 has factors: 2600837 real 34m58.010s user 34m57.090s sys 0m0.524s Code:
./pfgw64 tp q"10^1000010^34861" PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 10^1000010^34861 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) 10^1000010^34861 is prime! (3.8788s+0.0002s) ./pfgw64 tp q"10^1000010^39091" PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 10^1000010^39091 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) 10^1000010^39091 is prime! (3.8218s+0.0001s) ./pfgw64 tp q"10^1000010^51331" PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 10^1000010^51331 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) 10^1000010^51331 is prime! (3.9534s+0.0001s) ./pfgw64 tp q"10^1000010^79281" PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 10^1000010^79281 [N+1, BrillhartLehmerSelfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) 10^1000010^79281 is prime! (4.5040s+0.0002s) Last fiddled with by paulunderwood on 20201022 at 15:28 

20201022, 18:06  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·43·73 Posts 
Code:
      rank description digits who year comment       11538 10^38808010^1124331 388080 CH8 2014 Nearrepdigit (**) 11539 10^38808010^1808681 388080 p377 2014 Nearrepdigit 11540 10^38808010^3329441 388080 p377 2014 Nearrepdigit 11541 10^38808010^3420291 388080 p377 2014 Nearrepdigit 12104 10^37696810^1884841 376968 p404 2018 Nearrepdigit 12949 10^36036010^1830371 360360 p374 2014 Nearrepdigit 18009 10^27720010^990881 277200 p367 2013 Nearrepdigit 18010 10^27720010^1782311 277200 p367 2013 Nearrepdigit 18011 10^27720010^2577681 277200 p372 2013 Nearrepdigit 37645 10^13480910^674041 134809 p235 2010 Nearrepdigit, palindrome 41256 10^10428110^521401 104281 p16 2003 Nearrepdigit, palindrome 45524 10^10000010^614031 100000 p62 2001 Nearrepdigit ... Mathematical Description: ^10^%10^%1 Type: all Maximum number of primes to output: 300 There was an archived project  https://mersenneforum.org/forumdisplay.php?f=107 
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