The nth Prime Page
will now find any of the first 2,623,557,157,654,233 primes or
) for x
up to 100,000,000,000,000,000.
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:
|Description:||243112609 - 1|
|Verification status (*):||External|
|Official Comment:||Mersenne 47?|
|Unofficial Comments:||This prime has 3 user comments below.|
|Proof-code(s): (*):||G10 : Smith_E, GIMPS, Prime95|
|Decimal Digits:||12978189 (log10 is 12978188.5003329)|
|Rank (*):||3 (digit rank is 1)|
|Entrance Rank (*):||1|
|Currently on list? (*):||short|
|Submitted:||8/23/2008 01:33:38 CDT|
|Last modified:||1/16/2016 08:47:28 CDT|
|Score (*):||54.484 (normalized score 46883.1938)|
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
- Mersenne (archivable *)
- Prime on list: yes, rank 3
(archival tag id 187003, tag last modified 2016-01-19 07:57:44)
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.
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.
|machine||RedHat P4 P4|
|notes||Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 2 43112609 -1 2>&1|
[Elapsed time: 11.978 seconds]
|notes||This prime was first verified by Tom Duell (Burlington, MA, USA) and Rob Giltrap (Wellington, New Zealand), both of Sun Microsystems, using the Mlucas program by Ernst Mayer of Cupertino California USA. The verifications ran on 8 dual-core SPARC64 VI 2.15Ghz CPUs of a Sun SPARC Enterprise M5000 Server and 4 quad-core SPARC64 VII 2.52GHz CPUs of a Sun SPARC Enterprise M8000 Server in Menlo Park, CA, USA. The prime verification took 13 days.|
The prime was also independently verified by Tony Reix of Bull S.A. in Grenoble, France using 16 1.6 GHz Itanium2 CPUs of a Bull NovaScale 6160 HPC server and the Glucas program. Jeff Gilchrist of Carleton University in Ottawa, Canada has also verified the prime using up to 16 1.6 GHz Itanium2 CPUs of a server at SHARCNET, running the Glucas program by Guillermo Ballester Valor of Granada, Spain.
Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.