78 · 622402915 - 1

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:78 · 622402915 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L5645 : Orpen1, SRBase, LLR
Decimal Digits:1125662   (log10 is 1125661.9449423)
Rank (*):841 (digit rank is 1)
Entrance Rank (*):625
Currently on list? (*):short
Submitted:5/25/2023 07:28:10 UTC
Last modified:5/25/2023 16:37:14 UTC
Database id:136088
Status Flags:none
Score (*):46.9961 (normalized score 7.5396)

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_id136088
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tp -q"78*622^402915-1" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 78*622^402915-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 400K, Pass1=640, Pass2=640, clm=1 on 78*622^402915-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 39/3739369 ERROR: ROUND OFF 0.4585>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 420K, Pass1=960, Pass2=448, clm=1 on 78*622^402915-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 142542/3739369 ERROR: ROUND OFF 0.4511>0.45
(Test aborted, try again using the -a2 (or possibly -a0) switch)
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 432K, Pass1=1152, Pass2=384, clm=1 on 78*622^402915-1
Calling Brillhart-Lehmer-Selfridge with factored part 89.22%


78*622^402915-1 is prime! (29856.6855s+0.0142s)
[Elapsed time: 8.29 hours]
modified2023-05-25 15:46:39
created2023-05-25 07:29:02
id181918

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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