The Prime Database: (30^157950+1)^2-2

(30¹⁵⁷⁹⁵⁰ + 1)² - 2
(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 : User Comments : 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: (30¹⁵⁷⁹⁵⁰ + 1)² - 2

Verification status (*): Proven

Official Comment:

Unofficial Comments: This prime has 2 user comments below.

Proof-code(s): (*): p392 : Batalov, Cksieve, OpenPFGW

Decimal Digits: 466623 (log₁₀ is 466622.604365942)

Rank (*): 3269 (digit rank is 1)

Entrance Rank (*): 1771

Currently on list? (*): yes

Submitted: 5/22/2016 19:32:41 CDT

Last modified: 5/23/2016 07:03:19 CDT

Database id: 121686

Status Flags: TrialDiv

Score (*): 44.2928 (normalized score 1.3143)

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.

Serge Batalov writes (23 May 2016):
Kynea prime, near-square

David Broadhurst writes (15 Jun 2016):
Arbitrarily dubbed a Kynea prime by the original investigator in reference to a personal acquaintance. Several people have deprecated this practice.

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 121686

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(30^157950+1)^2-2" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing (30^157950+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.00% proof)

(30^157950+1)^2-2 is prime! (18999.3140s+0.0135s)
[Elapsed time: 5.28 hours]

modified 2017-01-27 05:57:11

created 2016-05-22 19:33:01

id 167324

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.