U(8478, 1, 17710) + U(8478, 1, 17709)
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: | U(8478, 1, 17710) + U(8478, 1, 17709) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Lehmer number |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | p452 : Propper, Batalov, CM, OpenPFGW |
| Decimal Digits: | 69567 (log10 is 69566.147981447) |
| Rank (*): | 58011 (digit rank is 1) |
| Entrance Rank (*): | 58001 |
| Currently on list? (*): | yes |
| Submitted: | 9/20/2025 22:53:09 UTC |
| Last modified: | 9/21/2025 18:37:14 UTC |
| Database id: | 141088 |
| Status Flags: | Verify |
| Score (*): | 38.4357 (normalized score 0.0007) |
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.
- Lehmer number (archivable *)
- Prime on list: yes, rank 1
Subcategory: "Lehmer number"
(archival tag id 239516, tag last modified 2025-09-21 18:37:16)
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 141088 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"lucasU(8478,1,17710)+lucasU(8478,1,17709)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing lucasU(8478,1,17710)+lucasU(8478,1,17709) [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2 on A 231094-bit number
Running N+1 test using discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 24K, Pass1=384, Pass2=64, clm=2 on A 231094-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 4031/234386 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 25K, Pass1=320, Pass2=80, clm=2 on A 231094-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 1088/234386 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a2 (or possibly -a0) switch)
Running N+1 test using discriminant 13, base 2+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 28K, Pass1=448, Pass2=64, clm=2 on A 231094-bit number
Calling N+1 BLS with factored part 0.27% and helper 0.17% (0.97% proof)
lucasU(8478,1,17710)+lucasU(8478,1,17709) is Fermat and Lucas PRP! (394.0967s+0.0042s)
[Elapsed time: 6.60 minutes]modified 2025-09-21 18:11:21 created 2025-09-21 18:04:45 id 187178
Query times: 0.0112 seconds to select prime, 0.0126 seconds to seek comments.
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