813 · 24335309 + 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: | 813 · 24335309 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L5476 : Steinbach, LLR2, PSieve, Srsieve, PrimeGrid, LLR |
| Decimal Digits: | 1305061 (log10 is 1305060.9595626) |
| Rank (*): | 976 (digit rank is 1) |
| Entrance Rank (*): | 963 |
| Currently on list? (*): | yes |
| Submitted: | 2/21/2026 20:17:43 UTC |
| Last modified: | 2/22/2026 23:37:15 UTC |
| Database id: | 141893 |
| Status Flags: | none |
| Score (*): | 47.4497 (normalized score 3.7737) |
User comments about this prime (disclaimer):
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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 141893 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"813*2^4335309+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 813*2^4335309+1 [N-1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 5
Special modular reduction using all-complex FMA3 FFT length 288K, Pass1=384, Pass2=768, clm=2 on 813*2^4335309+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
813*2^4335309+1 is prime! (9014.2908s+0.0011s)
[Elapsed time: 2.50 hours]modified 2026-02-22 22:51:10 created 2026-02-22 20:20:53 id 188082
Query times: 0.0003 seconds to select prime, 0.0006 seconds to seek comments.
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