Phil Carmody and I were playing strange base-10 games, in the wake of
http://listserv.nodak.edu/scripts/wa.exe?A2=ind0306&L=nmbrthry&P=R711
In comparison with those mind-bending exercises, it was rather
simple to improve on Hans Rosenthal's ECPP-intensive record
> (35*10^4157-53)/99 4157 c17 02 ECPP, palindrome
also noted in
http://primes.utm.edu/curios/page.php?number_id=1632
Until today, this was:
1) "The largest known prime with only two different prime digits"
and also, in the Dubner-Ondrejka base-10 olympic games:
2) the largest known palindromic prime with all of its digits prime.
Both of these records were surpassed in a few hours today, thanks
to a speedy search-and-proof routine enabled by OpenPFGW, and also
thanks to the Cunningham project, for a 40% factorization of
10^4260-1:
Primality testing
(30*R(15)+4)*R(4260)/R(15)-1
[N-1/N+1, Brillhart-Lehmer-Selfridge]
Calling N+1 BLS with factored part 40.35%
and helper 0.10% (121.17% proof)
(30*R(15)+4)*R(4260)/R(15)-1 is prime!
with a helper file
http://physics.open.ac.uk/~dbroadhu/cert/hd4260.fac
that enables the OpenPFGW proof
that the 4261-digit palindrome
33333333(333333373333333)_{283}33333333
is prime.
David Broadhurst