10³⁸⁸⁰⁸⁰ - 10¹¹²⁴³³ - 1

This prime's information:

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 31
Subcategory: "Near-repdigit"
(archival tag id 217849, tag last modified 2024-02-07 04:37:20)

User comments about this prime (disclaimer):

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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! Goodbye! ================TestSuite/380k1.in================ n = 10^388080-10^112433-1; F = 1; G = 10^112433 * (10^373-1) * 20693 * 42813227 * 78978409 * 669764569 * 36736831058062847438160876721; ================TestSuite/380k1.out================ 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.