689 · 21512316 - 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:689 · 21512316 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L2257 : Dettweiler, PSieve, Srsieve, NPLB, LLR
Decimal Digits:455256   (log10 is 455255.31714179)
Rank (*):6661 (digit rank is 1)
Entrance Rank (*):2794
Currently on list? (*):no
Submitted:6/5/2018 14:26:51 CDT
Last modified:6/5/2018 15:50:22 CDT
Removed (*):9/5/2020 09:18:55 CDT
Database id:125365
Status Flags:TrialDiv
Score (*):44.2171 (normalized score 0.7871)

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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"689*2^1512316-1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 689*2^1512316-1 [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: 19/1512327 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% 689*2^1512316-1 is prime! (2918.0769s+0.0008s) [Elapsed time: 48.63 minutes]
modified2020-07-07 17:30:14
created2018-06-05 14:33:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.