51989197414600215 · 267202 - 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: | 51989197414600215 · 267202 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Cunningham chain (4p+3) |
| Proof-code(s): (*): | L6373 : Karakai, Magyar, Farkas, Jarai, LLR |
| Decimal Digits: | 20247 (log10 is 20246.533681724) |
| Rank (*): | 77288 (digit rank is 1) |
| Entrance Rank (*): | 77276 |
| Currently on list? (*): | yes |
| Submitted: | 10/12/2026 09:48:02 UTC |
| Last modified: | 10/17/2026 00:37:12 UTC |
| Database id: | 142508 |
| Status Flags: | none |
| Score (*): | 34.6242 (normalized score 0) |
Archival tags:
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
- Cunningham Chains (1st kind) (archivable class *)
- Prime on list: yes, rank 1, weight 44.32376073048
Subcategory: "Cunningham chain (4p+3)"
(archival tag id 240456, tag last modified 2026-10-17 00:37:15)
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 142508 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"51989197414600215*2^67202-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 51989197414600215*2^67202-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 8K, Pass1=128, Pass2=64, clm=2 on A 67260-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 99.92%
51989197414600215*2^67202-1 is prime! (27.0001s+0.0001s)
[Elapsed time: 30.00 seconds]modified 2026-10-17 00:26:35 created 2026-10-17 00:26:05 id 188691
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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