The Prime Database: 5309*2^1257831+1

5309 · 2^1257831 + 1
(Another of the Prime Pages' resources)

GIMPS has discovered a new largest known prime number: 2^82589933-1 (24,862,048 digits)

For this prime : General Information : Verification Data :

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help) value

Description: 5309 · 2^1257831 + 1

Verification status (*): Proven

Official Comment:

Proof-code(s): (*): L3810 : Radle, PSieve, Srsieve, PrimeGrid, LLR

Decimal Digits: 378649 (log₁₀ is 378648.58548875)

Rank (*): 10419 (digit rank is 1)

Entrance Rank (*): 3030

Currently on list? (*): no

Submitted: 4/8/2014 13:05:05 CDT

Last modified: 4/8/2014 13:52:16 CDT

Removed (*): 4/29/2015 10:20:08 CDT

Database id: 117582

Status Flags: TrialDiv

Score (*): 43.651 (normalized score 0.7078)

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 117582

person_id 9

machine WinXP Dual Core 2.6GHz 64-bit Laptop

what prime

notes Command: pfgw64.exe -t -q"5309*2^1257831+1" 2>&1
PFGW Version 3.7.3.64BIT.20130210.Win_Dev [GWNUM 27.8]
Primality testing 5309*2^1257831+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
5309*2^1257831+1 is prime! (977.8271s+0.0023s)
[Elapsed time: 978 seconds]

modified 2014-04-14 15:25:10

created 2014-04-08 13:18:50

id 163116

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.