The Prime Database: 25*2^4481024+1

25 · 2^4481024 + 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 : Archival Tags : 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: 25 · 2^4481024 + 1

Verification status (*): Proven

Official Comment: Generalized Fermat

Unofficial Comments: This prime has 1 user comment below.

Proof-code(s): (*): L4364 : Steinbach, PSieve, Srsieve, PrimeGrid, LLR

Decimal Digits: 1348925 (log₁₀ is 1348924.0332302)

Rank (*): 171 (digit rank is 1)

Entrance Rank (*): 161

Currently on list? (*): short

Submitted: 10/12/2019 12:23:48 CDT

Last modified: 10/12/2019 14:20:22 CDT

Database id: 130014

Status Flags: TrialDiv

Score (*): 47.5511 (normalized score 32.4787)

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.

Generalized Fermat (archivable *)
Prime on list: no, rank 44
Subcategory: "Generalized Fermat"
(archival tag id 223547, tag last modified 2019-12-07 00:50:28)

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.

PrimeGrid writes (12 Oct 2019):
Divides xGF(4481020,8,5), xGF(4481021,11,9)

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 130014

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"25*2^4481024+1" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 25*2^4481024+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

25*2^4481024+1 is prime! (6449.1016s+0.0007s)
[Elapsed time: 1.79 hours]

modified 2019-10-12 14:18:30

created 2019-10-12 12:31:01

id 175699

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.