The trophy case table below shows first known occurances of super-dense k-tuples.
The first column shows the number of additional primes that can be packed in the
interval, as a contradiction to a Hardy-Littlewood conjecture.
Additions to the table can be posted by sending the residue sets or a listing of prime
for the width to be added. Please send any additions to tom(at)opertech.com
The 447-tuple was independently found by Ralph Gasser/Prof. Joerg Waldvogel, Mischa
Kenn, and Thomas J Engelsma
TE -- Thomas J Engelsma
JW-- Prof. Joerg Waldvogel
* -- created by Thomas J Engelsma from tuples submitted by Prof. Joerg Waldvogel
blank -- progress of searches by Thomas J Engelsma using sub-patterns from all existing
The links to the raw data are to ASCII text files. The data is in half-difference format.