MultiFactorial Prime Search

[rogue]

Originally Posted by henryzz

It sounds like it may be more sensible just to start over.

That is what I'm doing. It is a lot of rework. That is why I've asked for help. I have no idea when I'll be finished. I think I can finish all types to n=100000 by the end of the year, but that depends upon how many of my co-workers help. As for above n=100000, that is more difficult to gauge. Type 7 and 23 have been tested much further than other types, so it means a lot more time will be dedicated to sieving and testing. Fortunately I have sieved about half of the types 3 to 25 to appropriate depths, but will complete sieving all others (minus types 7 and 23) before I start testing the ranges. Type 7 will be absolutely terrible, so I've sent an e-mail to Rene Dohmen hoping that he kept residues for type 7.

[rogue]

Originally Posted by rogue

I have more bad news. I have tested to over 40,000 on each of the types. Of the 24 I'm testing, 17 are missing primes with a total of 21 of 48 with missing primes when including both + and -.

Make that 18. I just found a prime missed for type 2.

After much consideration, I have come to the conclusion that some users were running old copies of pfgw or maybe even primeform. It is a fact that older versions of pfgw/primeform had bugs that resulted in primes being found composite. I've seen that on the other projects where I have re-processed old ranges (generalized Cullen and Woodall). Any results prior my taking ownership (circle 2009) are likely suspect and most of the oldest work was done prior to that time.

[wombatman]

Type 16 has been tested up to n=210000.

The following PRPs were found:

102354!16+1
116340!16-1
116682!16+1
116942!16+1
118266!16+1
123066!16-1
126166!16+1
130200!16-1
145852!16+1
152818!16-1
166316!16+1
167328!16-1
195388!16-1
204430!16+1

I will continue on with types 24 and 25.

[rogue]

Thank you!

Although your results match known results for ranges known to be searched, you did find one unknown prime with 195388!16-1. That was beyond the known search range.

Are you still planning on searching 24 and 25?

[science_man_88]

with k=1 b= N%K; n=N\K; where \ is the floor of division and c, this is based on the fact that a multifactorial(N,K) is which when taken mod K are all the same value so form a power under modular arithmetic mod K. so mod K these values form the same as k*b^n+c.

[wombatman]

Originally Posted by rogue

Thank you!

Although your results match known results for ranges known to be searched, you did find one unknown prime with 195388!16-1. That was beyond the known search range.

Are you still planning on searching 24 and 25?

Yes indeed. I've got type 24 running now and am currently at n=~188,000. Once that's done (at n=300,000, if I recall correctly), I'll get type 25 finished up.

[rogue]

Originally Posted by science_man_88

with k=1 b= N%K; n=N\K; where \ is the floor of division and c, this is based on the fact that a multifactorial(N,K) is which when taken mod K are all the same value so form a power under modular arithmetic mod K. so mod K these values form the same as k*b^n+c.

Sorry that I'm being dense, but I fail to see how this will make sieving faster. Please walk me through an example sieving from 1000!7+1 thru 2000!7+1.

[rogue]

The entire range for !2 is now retested to 100,000. 76190!2-1 is a new prime that was missed by previous searches. I've been waiting to get to a milestone before posting the new search page. If I'm lucky, it will be reached this weekend.

[science_man_88]

Originally Posted by rogue

Sorry that I'm being dense, but I fail to see how this will make sieving faster. Please walk me through an example sieving from 1000!7+1 thru 2000!7+1.

I'm probably dense but I figured I'd mention it. also we know for example from this that mod 7 6^142+1 is congruent to 1000!7+1. we can use this and maybe a few other things ( like what the multiple of 7 is between them) to figure out. I guess I was mostly thinking of eliminating c values so I guess I'm just too stupid.

[Batalov]

Originally Posted by wombatman

I've got Base 24 running now and am currently at n=~188,000. Once that's done (at n=300,000, if I recall correctly), I'll get Base 25 finished up.

What are you guys calling "bases" here? Isn't it a misnomer? It is all over this thread.

I take it that you are referring to what Davis calls "types", i.e. how many numbers are skipped in a product series.

[rogue]

Originally Posted by Batalov

What are you guys calling "bases" here? Isn't it a misnomer? It is all over this thread.

I take it that you are referring to what Davis calls "types", i.e. how many numbers are skipped in a product series.

You are correct. I didn't notice his nomenclature and should have used it.

Outside of a few comments, I have make that change so you will see some posts have been edited.