MultiFactorial Prime Search

[chroma]

Originally Posted by rogue

I was not aware that you had resurrected the search. If your site is more complete than mine, then I can redirect to your site. Are you aware of all of the multifactorial primes that were missed by other searchers? Have you included those in your list?

On my webpage, I have put all Kevin's results. I have been verifying only the results of multifactorial primes with digits <= 10,000. I haven't verified the rest.

The list of all multifactorial primes I have tested by myself is included in the file:
http://mfprimes.republika.pl/Range_m...an_otremba.txt

I have also added your new results that were missing in mine and Kevin's data. IMHO the results on my page are complete.

Right now I am searching multifactorial primes (n!k+-1) with digits <= 10,000 and k = 102..200

[chroma]

Originally Posted by rogue

559741!7+1 is prime!

If I computed the length correctly, that is 424902 digits! Once submitted it will be around position 2800 in the Top 5000 and will set a new record for the form.

Congrats !
I verified this result

Primality testing 559741!7+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 79967
Calling Brillhart-Lehmer-Selfridge with factored part 33.95% 559741!7+1 is prime! (4675.2281s+2.1494s) (digits 424902) Mark Rodenkirch 02/2017

OK

[Batalov]

Originally Posted by rogue

559741!₇+1 is prime!

Because 7 | 559741, it can also be written as
559741!₇+1 = 79963! * 7⁷⁹⁹⁶³ + 1.

What values (mod 7) are left in the sieve, out of curiosity?
And why is it not submitted to UTM?

[rogue]

Originally Posted by Batalov

Because 7 | 559741, it can also be written as
559741!₇+1 = 79963! * 7⁷⁹⁹⁶³ + 1.

What values (mod 7) are left in the sieve, out of curiosity?
And why is it not submitted to UTM?

I do not understand your first question.

It is not submitted to UTM because this is not owned by me (even though it has my name) and I need to add mfsieve to it. Chris hasn't responded to me yet.

[Batalov]

Originally Posted by rogue

...because this is not owned by me (even though it has my name)

Wow! This is very unusual.
__ __ __ __ __ __

Re: first question.
Clearly, x!_m 1 has strong implications on the survivor values of x (mod m) after sieving with small primes.
Take m=2, for example. Can x be odd and x!₂ 1 prime? Clearly not (except for trivial 1!₂ + 1 and 3!₂ - 1, where both equal two 2, obviously. All other even numbers are not prime.).
Now, because x must be even, for the rest of the sieve, you get only (2x)!₂ 1,which is equal to x! * 2^x 1 which doesn't require an explanation what "!₂" or "!!" exactly is. Well, almost everyone knows what "!" means without an explanation.

So, my question was about the same for m=7. And because you have the sieve file, I expected just simple stats, not a theory. (Apparently I can exclude x=1 (mod 7) for the "-1" form.)
But that's ok; I left the m=7 sieve running and will have a look at my own copy of the sieve file tomorrow morning...

[axn]

Originally Posted by rogue

It is not submitted to UTM because this is not owned by me (even though it has my name) and I need to add mfsieve to it. Chris hasn't responded to me yet.

If that entry is going to be modified, it could always be done after the fact, can't it?

[rogue]

Originally Posted by axn

If that entry is going to be modified, it could always be done after the fact, can't it?

Yes, I will probably do that.

[chroma]

Originally Posted by Batalov

Because 7 | 559741, it can also be written as
559741!₇+1 = 79963! * 7⁷⁹⁹⁶³ + 1.

The same case holds for mfp+1 (n!7+1)
n -> (35 = 5*7, 49 = 7^2, 147 = 3*7^2, 336 = 2^4*3*7, 2079 = 3^3*7*11, 8855 = 5*7*11*23, 20636 = 2^2*7*11*67, 22988 = 2^2*7*821, 41139 = 3^2*7*653, 208502 = 2*7*53*281, 559741 = 7*13*6151)

and for mfp-1 (n!7-1)
n -> (14 = 2*7, 98 = 2*7^2, 371 = 7*53, 959 = 7*137, 4389 = 3*7*11*19, 10150 = 2*5^2*7*29, 13321 = 7*11*173, 54481 = 7*43*181, 61467 = 3*7*2927, 92288 = 2^7*7*103, 330925 = 5^2*7*31*61, 368851 = 7*23*29*79, 446236 = 2^2*7*15937)

[chroma]

A new record of largest multifactorial primes

220502!2+1 is prime! (digits: 541,239) SFukui 01/2017

http://primes.utm.edu/primes/page.php?id=122753

[rogue]

Originally Posted by chroma

A new record of largest multifactorial primes

220502!2+1 is prime! (digits: 541,239) SFukui 01/2017

http://primes.utm.edu/primes/page.php?id=122753

Nice.

[rogue]

FYI, I updated the first post to redirect to Marian's page.