- Torbjörn Alm has found the 3 largest known CPAP-7 (7 consecutive primes in
a*460# + x + 210n, n=0..6 (201 digits)
for a = 7032468079552, 7091037255023 and 7127829789350
where x is the 177-digit constant:
Congratulations to Torbjörn on this top-3!
He used my program and I also ran it but only found CPAP-6's.
The GMP library was used for prp testing.
All primes were proved with Tony Forbes' VFYPR.
The old CPAP-7 record was 97 digits but the new is larger than the 7-tuplet
record at 178 digits.
A CPAP-7 must have a multiple of 7# = 210 as the difference between the primes
to avoid divisibility by 2, 3, 5 and 7. This requires at least 209*6 = 1254
intermediate composites and would usually be harder than a 7-tuplet.
However the program computed a certain set of modular equations for all primes
<= 433 (the 4 extra primes up to 460 were not necessary). The constant x was
then computed to satisfy the equations. This guaranteed that the 1254 numbers
all had a factor <= 433, so any AP-7 would also be CPAP-7.
The expectation would be 6 days for my Athlon 1500+ alone. We were above
expectation for 3 monitored pc's when the only unmonitored pc was checked
after some days and showed 3 solutions!
Jens Kruse Andersen