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-   -   Primes made mostly of nines (https://www.mersenneforum.org/showthread.php?t=26116)

 fivemack 2020-10-22 10:47

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 ?

 xilman 2020-10-22 11:31

[QUOTE=fivemack;560683]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 ?[/QUOTE]Why do you care?

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

 kruoli 2020-10-22 11:34

FactorDB instantly proved it by N+1 as being prime.

 R. Gerbicz 2020-10-22 11:58

[QUOTE=fivemack;560683]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 ?[/QUOTE]

Combined Theorem 1 is enough from [url]https://primes.utm.edu/prove/prove3_3.html[/url]
with F1=1, F2=10^8668.

 fivemack 2020-10-22 13:33

[QUOTE=xilman;560687]Why do you care?

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

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)

 paulunderwood 2020-10-22 13:46

[QUOTE=fivemack;560683]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 ?[/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, 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) [/CODE]

:smile:

Back in the day, we found [URL="https://primes.utm.edu/primes/page.php?id=168"]this one[/URL] 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]

[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]

[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)

[/CODE]

 Batalov 2020-10-22 18:06

[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
...[/CODE]
[url]https://primes.utm.edu/primes/search.php[/url]
Mathematical Description: ^10^%-10^%-1
Type: all
Maximum number of primes to output: 300

There was an archived project - [url]https://mersenneforum.org/forumdisplay.php?f=107[/url]

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