2176177 + 60947
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: | 2176177 + 60947 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP |
| Proof-code(s): (*): | E11 : Karpovich, CM |
| Decimal Digits: | 53035 (log10 is 53034.561546093) |
| Rank (*): | 62959 (digit rank is 1) |
| Entrance Rank (*): | 62935 |
| Currently on list? (*): | yes |
| Submitted: | 11/23/2025 13:19:31 UTC |
| Last modified: | 11/26/2025 16:37:12 UTC |
| Database id: | 141258 |
| Status Flags: | Verify |
| Score (*): | 37.5988 (normalized score 0.0002) |
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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: yes, rank 7
Subcategory: "ECPP"
(archival tag id 239604, tag last modified 2025-11-26 16:37:14)
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 141258 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"2^176177+60947" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 2^176177+60947 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 2
Special modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on 2^176177+60947
Running N-1 test using base 3
Special modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on 2^176177+60947
Running N-1 test using base 7
Special modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on 2^176177+60947
Running N-1 test using base 11
Special modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on 2^176177+60947
Running N+1 test using discriminant 31, base 1+sqrt(31)
Special modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on 2^176177+60947
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
2^176177+60947 is Fermat and Lucas PRP! (414.0129s+0.0005s)
[Elapsed time: 6.92 minutes]modified 2025-11-26 16:16:44 created 2025-11-26 16:09:49 id 187348
Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.