51073006 - 5423800 - 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: | 51073006 - 5423800 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | [none] |
| Proof-code(s): (*): | p269 : Zhou, OpenPFGW |
| Decimal Digits: | 750000 (log10 is 749999.00847257) |
| Rank (*): | 4972 (digit rank is 1) |
| Entrance Rank (*): | 4948 |
| Currently on list? (*): | yes |
| Submitted: | 11/19/2025 15:47:06 UTC |
| Last modified: | 11/26/2025 05:37:10 UTC |
| Database id: | 141249 |
| Status Flags: | none |
| Score (*): | 45.7501 (normalized score 1.0172) |
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 141249 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tp -q"5^1073006-5^423800-1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 5^1073006-5^423800-1 [N+1, Brillhart-Lehmer-Selfridge]
trial
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 256K, Pass1=256, Pass2=1K, clm=2 on A 2491443-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 82/2491444 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 288K, Pass1=384, Pass2=768, clm=4 on A 2491443-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 39.50%
5^1073006-5^423800-1 is prime! (63477.2834s+0.0105s)
[Elapsed time: 17.63 hours]modified 2025-11-26 04:57:24 created 2025-11-25 11:19:26 id 187339
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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