685 · 21563423 - 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.

Description:685 · 21563423 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1817 : Barnes, PSieve, Srsieve, NPLB, LLR
Decimal Digits:470641   (log10 is 470640.05460154)
Rank (*):4405 (digit rank is 1)
Entrance Rank (*):4188
Currently on list? (*):yes
Submitted:7/20/2020 17:39:54 CDT
Last modified:7/20/2020 18:50:18 CDT
Database id:131031
Status Flags:TrialDiv
Score (*):44.3192 (normalized score 1.0971)

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_id131031
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/4/pfgw64 -tp -q"685*2^1563423-1" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 685*2^1563423-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 18/1563434 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


685*2^1563423-1 is prime! (3002.4808s+0.0010s)
[Elapsed time: 50.03 minutes]
modified2020-07-20 18:31:03
created2020-07-20 17:41:01
id176719

Query times: 0.0008 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.