Verifying a large prime gap can take as long as the original discovery. Most prime gaps in the top-20 tables for merit above 10 or 20 on July 15 2010 have been verified on independent hardware, except those with size 2254930, 2055816, 724248 and 494010. They have only been partially verified. All verifications used PrimeForm/GW for prp testing. This program was also used in the original discoveries since there is no efficient alternative for large numbers not of a special form.
Largest known prime gap
has information about the partial verification of the gap with size 2254930 (known
factors have been verified, but only a few prp tests).
For the gap with size 2055816, every 5th number without a small factor has been
verified composite with identical prp test residues in all cases.
verify1078180.txt
and verify1078180.zip has information about the
complete verification of the gap with size 1078180.
First known prime megagap
has information about the complete verification of the gap with size 1001548.
top20gaptests.zip contains information about
form and performed prp tests on gap ends for gaps with prp's around 10000,
21717 and 43429 digits.
The gaps around 21717 digits have verification information including factors and prp test
residues in verify21718digits.zip.
There is no online documentation for the verification of composites in the
remaining gaps. This could be repeated within a GHz day for
most of them.
Jens Kruse Andersen's The Top-20 Prime Gaps:
http://users.cybercity.dk/~dsl522332/math/primegaps/gaps20.htm
First known prime megagap:
http://users.cybercity.dk/~dsl522332/math/primegaps/megagap.htm
Largest known prime gap:
http://users.cybercity.dk/~dsl522332/math/primegaps/megagap2.htm
This page was created 2 June 2004 by Jens Kruse Andersen. Last updated 31 August
2010.
E-mail me with any comments.
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