k=22544089918041953*E(130) generates 216 known primes

[Kosmaj]

The discussion about Top-5000 cutoff moved to a new thread:

http://www.mersenneforum.org/showthread.php?t=18482

Originally Posted by Batalov

Sure thing. I emailed C.C. (and added a comment to the prime, too).

I put the asterisk in my morning message, but forgot to post the footnote. It is this:
_______________________
*Note that the Top-5000 cutoff plane will pass exactly 1,000,000 bits today or tomorrow. For the record, right now it is still at 999,400 bits' size, but the 1,290,000-bits abominable primes keep on pouring in. Mark my words Next state of the Top5000 database will be that all primes from position ~1,500 to 5,000 will be ~1,290,000 bits.

[robert44444uk]

The candidate is perhaps the first as well with 100 primes known wearing its base 4 mask. Interestingly out of the 212 primes found, 119 are translatable to base 4, and only 93 not.

I have a hunch that the mismatch is not random. Base 4 is an extremely interesting base to analyse. It is the first square base, and resultant on that no prime p has modulo of p-1.

Generalised cunningham chains in square bases provide longer chains, and I think this is related to the last statement.

[Thomas11]

I stopped the sieve for n=800-1000k at p=9.6T (which is more than optimal) and updated the zip file (22544.zip) in the top post.

Sieving n=1.03-2M is already in progress...

[Lennart]

Output logging to file pfgw.out
Primality testing 22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^587833-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX FFT length 60K, Pass1=320, Pass2=192 on A 587965-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^587833-1 is prime! (2335.9659s+0.0007s)

Lennart

[Antonio]

630000-635000 range completed - no primes.

[lsoule]

732-740 complete, no primes

[Lennart]

Primality testing 22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^549598-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX FFT length 60K, Pass1=320, Pass2=192 on A 549730-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131*2^549598-1 is prime! (1954.0706s+0.0007s)


Lennart

[Antonio]

Taking 740-742

[Lennart]

500,001-600,000 Complete
4 Primes found


Lennart

[robert44444uk]

Originally Posted by Lennart

500,001-600,000 Complete
4 Primes found


Lennart

Congrats to all the searchers, and well done Lennart. Let's get this done to 1 megabit and then we are in business with the top 5000.

[lsoule]

Taking 742-750