Problem Ten revisited

[Harvey563]

4500 thru 4599 done, reserving 4602 thru 4699 - went to * for 4571.

[Harvey563]

complete 4602 through 4699, went to * for 4672 and 4698.

[Harvey563]

4700 thru 4799 done, reserving 4800 thru 4899, went to * for 4776

[science_man_88]

Originally Posted by Harvey563

The Prime Puzzles and Problems Connection website has the following puzzle:

http://www.primepuzzles.net/puzzles/puzz_010.htm

It is conjectured that ""For every primorial p(k)# there is at least one p(j) from the primorial (1<=j<=k), such that at least one of the following expressions give us a prime :

N = p(k)# * p(j) + 1

N = p(k)# * p(j) - 1

N = p(k)# / p(j) + 1

N = p(k)# / p(j) - 1

(using the Caldwell’s nomenclature, p(k)#=p(1) x p(2) x p(3) x ... x p(k), p(1)=2, p(2)=3, p(3)=5, etc.)

I have verified this to p(3515) and am continuing the search. If you want to help, or know of a new prime fitting one of the above forms larger that p(3515),[and thus eliminates a p(k)#], please let me know. Mark Rodenkirch has recently has presieved ranges for this project up to p(5000), and I would be happy to email some to you.

We have a OpenPFGW script that tests p(k)#*p(j)+/-1; and skips to the next k when a prime is found. If no candidate of these forms is found, we then will check that k value for p(k)#/p(j)+/-1. At present, most candidates yield a prime for the * forms.

A typical yield is 5 or 6 primes per day per core. I'll plan on sending you groups of ten k values, and note reservations here. You can just send me the primes found, or post them here.

I'll credit you as a contributor, & if you're lucky, you'll discover the k value that disproves the conjecture!

The project page is at http://harvey563.tripod.com/puzzle10.html

I was thinking of making a PARI code for this but I want to see if I can speed it up first, are there only limit congruency classes ( I think that's what the modular stuff is) for P(k)# ? if so what are they that can help determine what P(j) would have to follow to make the equation be either 6n+1 or 6n-1 (the forms of all primes greater than 3).

[Citrix]

Does the above conjecture hold for twin primes and other prime types. Anyone test this. I suspect, it would have to be more candidates per search term for it to be true for twins. Thanks.

[Harvey563]

4800 thru 4899 done, reserving 4900 thru 4999, only went to * for 4893.

[rogue]

Originally Posted by Harvey563

4800 thru 4899 done, reserving 4900 thru 4999, only went to * for 4893.

I will start sieving a higher range in the next few days. Any opinions on the upper bound of such a search?

[Harvey563]

I opine that up to p(6000) would be adequate, but I would have predicted a hit before now anyhow.

[rogue]

Originally Posted by Harvey563

I opine that up to p(6000) would be adequate, but I would have predicted a hit before now anyhow.

Did you want to do any sieving yourself? I have a few changes to the source to address building on other platforms.

[Harvey563]

I would be happy to sieve some, & I can do it in Windows or Linux.
(Although I can only compile in Linux.)

Steven

[rogue]

Originally Posted by Harvey563

I would be happy to sieve some, & I can do it in Windows or Linux.
(Although I can only compile in Linux.)

I cannot build a Windows exe with Visual Studio. I might be able to with MinGW. Do you have 64-bit or 32-bit Windows?