Here's why we double-check...

[gd_barnes]

Here is an excellent example of why we double check:

To the best of our knowledge, high-weight k=945 had been previously searched up to n=260K as of 8/15/04. An error had already been found in our double-check up to n=100K. A prime reported at n=21062 is actually n=31062. This was corrected many months ago on Karsten's rieselprime.org pages. We are still working with Michael Hartley on some corrections for Prime Search.

Subsequent to this, a prime was reported to the top-5000 site at n=350126 on 10/6/07 thru the old 15K project, which apparently is still running in some form.

The above might lead one to assume that the k had been searched contiguously past n>350K. That would be a poor assumption. NPLB has already found TWO top-5000 primes for n<350K!!:

945*2^342774-1 found by Chris (Flatlander) on 2/3
945*2^349086-1 found by me today (2/11)
:surprised

Clearly someone either started their testing at n=350K or possibly did a fixed-n search and in doing so missed 2 out of 3 primes of a very nice run in a range of n<7500.

So there you have it...


Gary