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: 10130048 + (9 · 1037077 - 2)/11 · 1046486 + 1 Verification status (*): Proven Official Comment: Tetradic palindrome Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): p235 : Bedwell, OpenPFGW Decimal Digits: 130049   (log10 is 130048) Rank (*): 26108 (digit rank is 2) Entrance Rank (*): 2375 Currently on list? (*): short Submitted: 9/28/2008 06:53:41 CDT Last modified: 9/28/2008 11:44:06 CDT Database id: 85568 Status Flags: none Score (*): 40.3635 (normalized score 0.0835)

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.

Tetradic (deprecated *)

Prime on list: no, rank 2
Subcategory: "Tetradic"
(archival tag id 187475, tag last modified 2009-09-08 14:50:32)

Palindrome (archivable *)

Prime on list: yes, rank 18
Subcategory: "Palindrome"
(archival tag id 187474, tag last modified 2013-01-08 06:50:30)

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.

David Broadhurst writes (28 Sep 2008): 

The decimal expansion of this prime is 1(0)_{46485}(81)_{18538}8(0)_{46485}1 where the subscripts indicate repetition of the strings 0 and 81.

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 85568 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"10^130048+(9*10^37077/11)*10^46486+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 10^130048+(9*10^37077/11)*10^46486+1 1/1 trial factoring to 45125533 10^130048+(9*10^37077/11)*10^46486+1 has no small factor. [Elapsed time: 437.022 seconds] modified 2011-12-27 16:48:46 created 2008-09-28 07:05:02 id 100605

field value prime_id 85568 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"10^130048+(9*10^37077/11)*10^46486+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 10^130048+(9*10^37077/11)*10^46486+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 864030 bit request FFT size=(57344,16) Running N-1 test using base 31 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 864030 bit request FFT size=(57344,16) Calling Brillhart-Lehmer-Selfridge with factored part 35.75% 10^130048+(9*10^37077/11)*10^46486+1 is prime! (6459.8197s+0.2008s) [Elapsed time: 1.79 hours] modified 2008-11-16 12:15:22 created 2008-09-28 07:08:02 id 100606