10388080 - 10112433 - 1

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:10388080 - 10112433 - 1
Verification status (*):PRP
Official Comment (*):Near-repdigit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH8 : Batalov, Ksieve, TOPS, LLR, OpenPFGW, CHG
Decimal Digits:388080   (log10 is 388080)
Rank (*):14527 (digit rank is 1)
Entrance Rank (*):3563
Currently on list? (*):no
Submitted:11/8/2014 14:15:17 CDT
Last modified:11/8/2014 18:50:29 CDT
Database id:118734
Status Flags:Verify, TrialDiv
Score (*):43.7266 (normalized score 0.3945)

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.
Near-repdigit (archivable *)
Prime on list: no, rank 29
Subcategory: "Near-repdigit"
(archival tag id 217849, tag last modified 2022-08-21 12:37:11)

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 (9 Nov 2014):  (report abuse)
   new stack size = 9227468800 (8800.000 Mbytes).
   realprecision = 131008 significant digits (131000 digits displayed)

Welcome to the CHG primality prover!

Input file is:  TestSuite/380k1.in
Certificate file is:  TestSuite/380k1.out
Found values of n, F and G.
    Number to be tested has 388080 digits.
    Modulus has 112864 digits.
Modulus is 29.082466484658430580% of n.

NOTICE: This program assumes that n has passed
    a BLS PRP-test with n, F, and G as given.  If
    not, then any results will be invalid!

Square test passed for G >> F.  Using modified right endpoint.

Search for factors congruent to 1.
    Running CHG with h = 6, u = 2. Right endpoint has 49491 digits.
        Done!  Time elapsed:  17835736ms.
    Running CHG with h = 6, u = 2. Right endpoint has 42766 digits.
        Done!  Time elapsed:  16030569ms.
    Running CHG with h = 5, u = 1. Right endpoint has 25952 digits.
        Done!  Time elapsed:  2478002ms.
A certificate has been saved to the file:  TestSuite/380k1.out

Running David Broadhurst's verifier on the saved certificate...

Testing a PRP called "TestSuite/380k1.in".

Pol[1, 1] with [h, u]=[4, 1] has ratio=1.1617062696639731125 E-62082 at X, 
          ratio=1.0649471820469185260 E-59670 at Y, witness=3.
Pol[2, 1] with [h, u]=[6, 2] has ratio=4.600208881862200351 E-1982 at X, 
          ratio=1.5538500063459444963 E-33628 at Y, witness=3.
Pol[3, 1] with [h, u]=[6, 2] has ratio=1.5538500063459444963 E-33628 at X, 
          ratio=7.525990010999927893 E-13452 at Y, witness=3.

Validated in 4 sec.

Congratulations! n is prime!
n = 10^388080-10^112433-1;
F = 1;
G = 10^112433 * (10^373-1) * 20693 * 42813227 * 78978409 * 669764569 * 36736831058062847438160876721;
Full output and certificate are available (80Kb, zipped). 
Note: F=1 deliberately, to make the proof shorter (one pass).

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tp -q"10^388080-10^112433-1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 10^388080-10^112433-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 28.98% 10^388080-10^112433-1 is Lucas PRP! (9046.8936s+0.0097s) [Elapsed time: 2.51 hours]
modified2020-07-07 17:30:17
created2014-11-08 15:58:47

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.