Generalized Cullen and Woodall Searches

[YaoPlaysMC]

I'm reserving 12 because numbers in this sequence are considered to be Proth numbers also. (n*12^n+1)

[rogue]

I have contacted both Steven Harvey and Gunther Loh. They are both still managing these searches. Please reach out to them to coordinate your reservations.

[YaoPlaysMC]

Is it okay if I take back my reservation without actually doing any primality tests, or if I do the reservation, do I have to finish all of the work before releasing it?

[rogue]

Originally Posted by YaoPlaysMC

Is it okay if I take back my reservation without actually doing any primality tests, or if I do the reservation, do I have to finish all of the work before releasing it?

This thread is not used for managing reservations. If you reserved thru Steven or Gunther, then you can unreserve thru them.

[YaoPlaysMC]

I just want to see how long a primality test would take using LLR but I can't seem to use the files from the sieving program in LLR? Can anyone find a way to primality test Gen. Cullen primes?


Edit: I found out that you can use openPFGW to primality test these primes.

[carpetpool]

Originally Posted by YaoPlaysMC

I just want to see how long a primality test would take using LLR but I can't seem to use the files from the sieving program in LLR? Can anyone find a way to primality test Gen. Cullen primes?


Edit: I found out that you can use openPFGW to primality test these primes.

You can test them with LLR, you will just need to format your candidates to a NewPGEN type header. Here is an example for n*3^n+1:

200000:P:1:3:257
32 32
34 34
54 54
76 76
114 114
128 128
176 176
202 202
212 212
252 252
274 274
308 308
318 318
390 390
414 414
470 470
474 474
516 516
532 532
534 534
548 548
580 580
620 620
634 634
688 688
694 694
800 800
812 812
860 860
894 894
898 898
900 900
902 902
968 968
974 974
980 980
988 988

[LaurV]

From srXsieve package, you can use srfile.exe to convert your sieve files to (almost) any format (like abc, abcd, pfgw, newpgen, etc), and put them in a form digested by LLR after just few trials, without much background knowledge.

[rogue]

Originally Posted by YaoPlaysMC

I just want to see how long a primality test would take using LLR but I can't seem to use the files from the sieving program in LLR? Can anyone find a way to primality test Gen. Cullen primes?


Edit: I found out that you can use openPFGW to primality test these primes.

llr would be faster and I thought that it supported the ABC format output by gcwsieve. I'll have to take a look at llr source.

Upon review, llr supports the ABC header of "$a*$b^$a$c", but gcwsieve outputs "$a*<base>^$a$b". It shouldn't be hard to modify gcwsieve to output an llr compatible ABC format. Until I do that you have other options to modify the file so that llr can use it.

[YaoPlaysMC]

For b=12 I found a new prime (345951*12^345951+1). Almost made the top 20 generalized Cullen primes.

Special modular reduction using zero-padded AVX-512 FFT length 144K, Pass1=192, Pass2=768, clm=1 on 345951*12^345951+1
Calling Brillhart-Lehmer-Selfridge with factored part 55.79%
345951*12^345951+1 is prime! (488.4216s+0.0016s)

[Batalov]

Originally Posted by carpetpool

You can test them with LLR, you will just need to format your candidates to ...

...any appropriate format.
Format ABC $a*$b^$c$d covers pretty much everything.