Phi(1203, 1027)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:Phi(1203, 1027)
Verification status (*):PRP
Official Comment (*):Unique, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c47 : Chandler, Primo
Decimal Digits:21600   (log10 is 21600)
Rank (*):72668 (digit rank is 1)
Entrance Rank (*):67888
Currently on list? (*):short
Submitted:11/11/2021 14:08:28 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132925
Status Flags:Verify
Score (*):34.8243 (normalized score 0)

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 79
Subcategory: "ECPP"
(archival tag id 226446, tag last modified 2024-03-24 06:37:14)
Unique (archivable *)
Prime on list: yes, rank 7
Subcategory: "Unique"
(archival tag id 226447, tag last modified 2023-05-15 15:37:15)

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.

Ray Chandler writes (11 Nov 2021):  (report abuse)
Phi(32481,10) = Phi(1203,10^27) = (10^21654+10^10827+1)/(10^54+10^27+1) PRP: Matthew Peets, November 12, 2008 Proven: Primo 4.3.3 - LX64, Nov 7, 2021 Verified: http://factordb.com/cert.php?id=1100000000556949265

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.
fieldvalue
prime_id132925
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"Phi(1203,10^27)" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing Phi(1203,10^27) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 43 Running N-1 test using base 59 Calling Brillhart-Lehmer-Selfridge with factored part 1.37% Phi(1203,10^27) is PRP! (18.4615s+0.1372s) [Elapsed time: 18.00 seconds]
modified2022-07-11 18:21:45
created2021-11-11 14:11:01
id178638

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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