6 · 878281137 - 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: | 6 · 878281137 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | A68 : Schroeder3, Srsieve, CRUS, PRST |
| Decimal Digits: | 827526 (log10 is 827525.99586954) |
| Rank (*): | 5258 (digit rank is 1) |
| Entrance Rank (*): | 4958 |
| Currently on list? (*): | no |
| Submitted: | 2/16/2026 11:41:09 UTC |
| Last modified: | 2/16/2026 21:37:13 UTC |
| Removed (*): | 2/19/2026 13:28:52 UTC |
| Database id: | 141786 |
| Status Flags: | none |
| Score (*): | 46.052 (normalized score 0.8313) |
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.
field value prime_id 141786 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"6*878^281137-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 6*878^281137-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using FMA3 FFT length 256K, Pass1=256, Pass2=1K, clm=2 on 6*878^281137-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 70/2748983 ERROR: ROUND OFF 0.5>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 FMA3 FFT length 288K, Pass1=384, Pass2=768, clm=4 on 6*878^281137-1
Calling Brillhart-Lehmer-Selfridge with factored part 89.77%
6*878^281137-1 is prime! (20721.1879s+0.0091s)
[Elapsed time: 5.76 hours]modified 2026-02-16 20:42:26 created 2026-02-16 14:57:02 id 187975
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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