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 2020-10-22, 10:47 #1 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 6,323 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 ?
2020-10-22, 11:31   #2
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

5·2,039 Posts

Quote:
 Originally Posted by fivemack 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 ?
Why do you care?

It isn't that 10k-digit numbers are difficult to prove prime by ECPP or APR-CL these days.

 2020-10-22, 11:34 #3 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 24·23 Posts FactorDB instantly proved it by N+1 as being prime.
2020-10-22, 11:58   #4
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

141710 Posts

Quote:
 Originally Posted by fivemack 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 ?
Combined Theorem 1 is enough from https://primes.utm.edu/prove/prove3_3.html
with F1=1, F2=10^8668.

2020-10-22, 13:33   #5
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

6,323 Posts

Quote:
 Originally Posted by xilman Why do you care? It isn't that 10k-digit numbers are difficult to prove prime by ECPP or APR-CL these days.
Using a gigahertz-month of compute for something which can sensibly be asserted by inspection would get probably ruder remarks from you and RDS :)

(my housemate had found a tweet getting excited about a 6400-digit prime comprised entirely of nines with a single eight, and I thought this was not a particularly exciting result)

2020-10-22, 13:46   #6
paulunderwood

Sep 2002
Database er0rr

1101101011102 Posts

Quote:
 Originally Posted by fivemack 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 ?
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, Brillhart-Lehmer-Selfridge]
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 10^10000-10^\$a-1
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.

10^10000-10^750-1 has factors: 2313617
10^10000-10^1589-1 has factors: 2635553
10^10000-10^3486-1 is 3-PRP! (1.1229s+0.0885s)
10^10000-10^3909-1 is 3-PRP! (1.0102s+0.1867s)
10^10000-10^4151-1 has factors: 376769
10^10000-10^5133-1 is 3-PRP! (1.0614s+0.0897s)
10^10000-10^5334-1 has factors: 772147
10^10000-10^6134-1 has factors: 2749921
10^10000-10^7928-1 is 3-PRP! (1.1574s+0.1369s)
10^10000-10^8072-1 has factors: 2742227
10^10000-10^8668-1 is 3-PRP! (0.9757s+0.0931s)
10^10000-10^8740-1 has factors: 2600837

real	34m58.010s
user	34m57.090s
sys	0m0.524s
Code:
./pfgw64 -tp -q"10^10000-10^3486-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^3486-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^3486-1 is prime! (3.8788s+0.0002s)

./pfgw64 -tp -q"10^10000-10^3909-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^3909-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^3909-1 is prime! (3.8218s+0.0001s)

./pfgw64 -tp -q"10^10000-10^5133-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^5133-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^5133-1 is prime! (3.9534s+0.0001s)

./pfgw64 -tp -q"10^10000-10^7928-1"
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]

Primality testing 10^10000-10^7928-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
10^10000-10^7928-1 is prime! (4.5040s+0.0002s)

Last fiddled with by paulunderwood on 2020-10-22 at 15:28

 2020-10-22, 18:06 #7 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23·5·229 Posts Code: ----- -------------------------------- ------- ----- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ----- ---- -------------- 11538 10^388080-10^112433-1 388080 CH8 2014 Near-repdigit (**) 11539 10^388080-10^180868-1 388080 p377 2014 Near-repdigit 11540 10^388080-10^332944-1 388080 p377 2014 Near-repdigit 11541 10^388080-10^342029-1 388080 p377 2014 Near-repdigit 12104 10^376968-10^188484-1 376968 p404 2018 Near-repdigit 12949 10^360360-10^183037-1 360360 p374 2014 Near-repdigit 18009 10^277200-10^99088-1 277200 p367 2013 Near-repdigit 18010 10^277200-10^178231-1 277200 p367 2013 Near-repdigit 18011 10^277200-10^257768-1 277200 p372 2013 Near-repdigit 37645 10^134809-10^67404-1 134809 p235 2010 Near-repdigit, palindrome 41256 10^104281-10^52140-1 104281 p16 2003 Near-repdigit, palindrome 45524 10^100000-10^61403-1 100000 p62 2001 Near-repdigit ... https://primes.utm.edu/primes/search.php 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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