532 Prime Grid

[Batalov]

And here's where you wanted to stop
5*3^214250+2 (102224 digits)
Glad to help!

[spkarra]

I uploaded the file that contains the results that I got from my Java code. I would be glad if it gets cross-checked.
Just export into MS-EXCEL 2003 or higher version - use ";" and "tab" as the delimiters. The numbers are very big so make sure that the columns are WRAP-TEXT.

[Batalov]

Plus and Minus OEIS series.

AUTHOR Robert G. Wilson v, Dec 26 2000

[spkarra]

Thanks Batalov.

So, the additional ones that I had are:

5*3^5124 Minus 2 ; Length ; 2446
5*3^5750 Minus 2 ; Length ; 2745
5*3^7616 Minus 2 ; Length ; 3635


5*3^7702 Plus 2 ; Length ; 3676
5*3^8823 Plus 2 ; Length ; 4211

Just FYI....I haven't found anything as of now..I am testing with n=10053.

[kar_bon]

Originally Posted by spkarra

Thanks Batalov.

So, the additional ones that I had are:

But you also missed two on the -1-side: n=2719, 3298.

[Batalov]

Originally Posted by kar_bon

But you also missed two on the -1-side: n=2719, 3298.

I actually submitted extensions to OEIS (up to n<=35000), and only now noticed that, indeed, these two are simply wrong in the sequence:
5*3^2719-2 has factors: 13
5*3^3298-2 has factors: 13

P.S. The minus sequence has no primes from 11328<n<=50000 ! I am running it to 100000. The large PRP for the plus side is shown earlier in this thread.

-S

[Batalov]

Ok, there it is; the gap was not endless.
The next "minus 2" PRP is
5*3^54287-2 (25903 digits)

[gd_barnes]

Originally Posted by kar_bon

But you also missed two on the -1-side: n=2719, 3298.

Serge is correct about n=2719 & 3298. After a bit of analysis to determine where these exponents would make a comparable form prime:

2*3^2719-5 is prime
2*3^3298-5 is prime

2*3^n-5 is the only form like k*b^n-/+c where k, b, & c are all <=10 that makes the form prime for n=2719 and 3298.

Karsten, as you probably know, we're testing 5*3^n-/+2 as opposed to 2*3^n-/+5.

[Batalov]

Gary, Karsten was merely pointing to the errors in OIES (at the time quoted), I think.
I think Neil will fix that on Monday. (I have yet another PRP for him, n~=57K, but I decided to stop after two messages. I know that some people hate piece mail. I'll submit the extension later, after this extension gets posted.)

[gd_barnes]

Originally Posted by Batalov

Gary, Karsten was merely pointing to the errors in OIES (at the time quoted), I think.
I think Neil will fix that on Monday. (I have yet another PRP for him, n~=57K, but I decided to stop after two messages. I know that some people hate piece mail. I'll submit the extension later, after this extension gets posted.)

OK, thanks. That wasn't very clear by Karsten's response. When he says that two are "missing" and there are actually two extras in the OEIS DB in the form that we are talking about in this thread, he needs to say as much. Obviously he confused you too because you tested the 5*3^n-2 forms and found the factor of 13 for them.

BTW, I deleted my last posting and your response where I was confused to avoid confusing others.

[spkarra]

Originally Posted by Mini-Geek

I don't know of a built-in function IsPrime that proves primality. There's an isProbablePrime under BigInteger, but that's just PRP, not proven. Can you please show us the code (or at least part of it, e.g. a description explaining it) you used to 'prove' these primes.
Java isn't the fastest way to prove these numbers, and the larger ones (unless I'm missing a faster option than ECPP with Primo) will take on the order of hours to days to prove.

I used BigInteger.IsProbablePrime(int certainity). To baseline my tests, I ran with the know Primes.

For Mersenne Prime 2^9941 - 1 (2993 digits long) the above Java Function took 2mins 47 secs.
For 2^11213-1 (3376) it took 4mins.
For 2^21701 - 1(6533) it took 29 mins 28 secs.
For 2^44497 - 1 (13395), NOTHING resulted even after running for 2 hrs.

That means, with the computing capacity that I have, I will try to find the 532 Grid upt0 7000 digits long.

As of today, I did upto 4500 digits.