"τ(6731018)"
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: | "τ(6731018)" |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP |
| Unofficial Comments: | This prime has 3 user comments below. |
| Proof-code(s): (*): | c65 : Lygeros, Rozier, Primo |
| Decimal Digits: | 15834 (log10 is 15833.723095781) |
| Rank (*): | 76472 (digit rank is 1) |
| Entrance Rank (*): | 58150 |
| Currently on list? (*): | no |
| Submitted: | 7/27/2013 12:44:14 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 114802 |
| Blob database id: | 297 |
| Status Flags: | Verify |
| Score (*): | 33.8635 (normalized score 0) |
Description: (from blob table id=297)
This number is tau(673^1018) and is one of the values discussed in the paper "Odd prime values of the Ramanujan tau function" by Nik Lygeros and Olivier Rozier [LR2013]. Patrice Deloche completed the proof using Primo. It is equal to the generalized Lucas number U(4741198635421922, 673^11, 1019).
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: no, rank 154
Subcategory: "ECPP"
(archival tag id 217204, tag last modified 2024-04-24 05:37:25)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 114802 person_id 9 machine WinXP Dual Core 2.6GHz 64-bit Laptop what prp notes Command: pfgw64.exe -tc p_114802.txt 2>&1 PFGW Version 3.7.3.64BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing 5285618102...6582063387 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.08% and helper 0.07% (0.30% proof) 5285618102...6582063387 is Fermat and Lucas PRP! (23.3288s+0.0527s) [Elapsed time: 23 seconds] modified 2020-07-07 22:30:18 created 2013-07-27 12:47:42 id 159980
field value prime_id 114802 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 5285618102237179....1825996582063387 1/1 mro=0 trial factoring to 4718812 5285618102...6582063387 has no small factor. [Elapsed time: 54.182 seconds] modified 2020-07-07 22:30:18 created 2013-07-27 12:48:02 id 159981
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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