February 17 Milton L. Brown wrote:
> The following PRP's produce a prime number gap of 398,370
>
> 10^14173+347173
> 10^14173-51197

Congratulations!
The merit of the gap is 398370 / log(10^14173-51197) = 12.21.
After years with smaller merits, you finally got a large gap
qualifying for http://hjem.get2net.dk/jka/math/primegaps/gaps20.htm

This is by far the largest gap with merit>10 and "basic" expression
(short expression with +-*/^, but not !#).
My old record from 2003 was a gap of 84630 after PRP3039 = 2^10093-
80445, with merit 12.10.

My rough heuristics say: The chance that the gap crossing a random
number (10^n for integer n qualifies) has merit>12 is around 1 in
e^12/12 = 1 in 13563. Most large gaps are found around non-random
numbers.

Thanks to Torbjörn Alm for verifying the gap with PrimeForm.

--
Jens Kruse Andersen