17484430616589 · 254201 + 5
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: | 17484430616589 · 254201 + 5 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Consecutive primes arithmetic progression (3,d=6), ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | E14 : Batalov, EMsieve, CM |
| Decimal Digits: | 16330 (log10 is 16329.369446477) |
| Rank (*): | 76647 (digit rank is 1) |
| Entrance Rank (*): | 76400 |
| Currently on list? (*): | short |
| Submitted: | 6/27/2024 08:48:11 UTC |
| Last modified: | 6/28/2024 08:37:17 UTC |
| Database id: | 138256 |
| Status Flags: | Verify |
| Score (*): | 33.9589 (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.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: yes, rank 1
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 229572, tag last modified 2024-06-28 08:37:19)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 120, weight 39.780523902928
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 229573, tag last modified 2024-06-28 08:37:22)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 150
Subcategory: "ECPP"
(archival tag id 229574, tag last modified 2024-07-27 21:37:12)
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 138256 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"17484430616589*2^54201+5" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 17484430616589*2^54201+5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 2
Special modular reduction using generic reduction FMA3 FFT length 5K on 17484430616589*2^54201+5
Running N+1 test using discriminant 5, base 5+sqrt(5)
Special modular reduction using generic reduction FMA3 FFT length 5K on 17484430616589*2^54201+5
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 33/54278 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 5, base 5+sqrt(5)
Special modular reduction using generic reduction FMA3 FFT length 6K, Pass1=128, Pass2=48, clm=2 on 17484430616589*2^54201+5
Calling N-1 BLS with factored part 0.07% and helper 0.03% (0.25% proof)
17484430616589*2^54201+5 is Fermat and Lucas PRP! (20.6555s+0.0002s)
[Elapsed time: 25.00 seconds]modified 2024-06-28 08:20:07 created 2024-06-28 08:19:41 id 184098
Query times: 0.0023 seconds to select prime, 0.0176 seconds to seek comments.
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