"τ(1572206)"
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(1572206)" |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP |
| Unofficial Comments: | This prime has 3 user comments below. |
| Proof-code(s): (*): | FE1 : Morain, FastECPP |
| Decimal Digits: | 26643 (log10 is 26642.780582553) |
| Rank (*): | 71432 (digit rank is 1) |
| Entrance Rank (*): | 40675 |
| Currently on list? (*): | no |
| Submitted: | 4/3/2011 |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 104821 |
| Blob database id: | 276 |
| Status Flags: | Verify |
| Score (*): | 35.4729 (normalized score 0) |
Description: (from blob table id=276)
This number is tau(157^2206) and is one of the values discussed in the paper "Odd prime values of the Ramanujan tau function" by Nik Lygeros and Olivier Rozier [NO2013]. François Morain completed the primality proof.Η ομάδα των N. Lygeros, F. Morain και O. Rozier ανακάλυψε και πιστοποίησε ένα πρώτο αριθμό 26.643 ψηφίων με τη μέθοδο των ελλειπτικών καμπυλών. Αυτό το επίτευγμα αποτελεί ένα νέο παγκόσμιο ρεκόρ στο τομέα της πιστοποίησης ενός άγνωστου πρώτου αριθμού με ένα γενικό αλγόριθμο. Το προηγούμενο παγκόσμιο ρεκόρ ήταν του Οκτωβρίου 2010 με 25.050 ψηφία. Το νέο ρεκόρ χρειάστηκε 1963 ημέρες υπολογισμών και 392 ημέρες πιστοποίησης, δηλαδή περίπου 6 ½ χρόνια συνολικών υπολογισμών σε ένα υπολογιστή. Η υλοποίηση έγινε σ' ένα δίκτυο bi - core i7 quad - core και τελείωσε στις 3 Απριλίου 2011. (from http://gdailynews.files.wordpress.com/2011/04/ceb1cebdceb1cebacebfceafcebdcf89cf83ceb7.pdf)
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 49
Subcategory: "ECPP"
(archival tag id 215622, tag last modified 2024-10-27 10:37:10)
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 104821 person_id 9 machine RedHat Virtual STEM Server what prp notes PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 6033683878...9490003443 [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 0.04% and helper 0.02% (0.13% proof) 6033683878...9490003443 is Fermat and Lucas PRP! (180.5058s+0.0312s) [Elapsed time: 3.17 minutes] modified 2020-07-07 22:30:28 created 2012-02-20 00:32:06 id 139233