(102332974 + 1)2 - 2

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

Description:(102332974 + 1)2 - 2
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p405 : Propper, Cksieve, OpenPFGW
Decimal Digits:4665949   (log10 is 4665948)
Rank (*):48 (digit rank is 1)
Entrance Rank (*):48
Currently on list? (*):short
Submitted:2/20/2024 13:05:54 UTC
Last modified:3/29/2024 14:37:18 UTC
Database id:137497
Status Flags:none
Score (*):51.3538 (normalized score 593.6927)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
fieldvalue
prime_id137497
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tc -q"(10^2332974+1)^2-2" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (10^2332974+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1 on A 15499944-bit number
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1 on A 15499944-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 39/15499951 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 1680K, Pass1=448, Pass2=3840, clm=2 on A 15499944-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 947/15499951 ERROR: ROUND OFF 0.48438>0.45
(Test aborted, try again using the -a2 (or possibly -a0) switch)
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 1728K, Pass1=768, Pass2=2304, clm=1 on A 15499944-bit number
Running N+1 test using discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 1600K, Pass1=640, Pass2=2560, clm=1 on A 15499944-bit number
Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.00% proof)


(10^2332974+1)^2-2 is prime! (3269692.5325s+0.0728s)
[Elapsed time: 37.84 days]
modified2024-03-29 13:40:35
created2024-02-20 17:25:37
id183339

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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