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2021-06-08, 07:20   #1
Alfred

May 2013
Germany

10101112 Posts
10^n+7: four PRPs

I've found four probable primes in the range 200001 <= n <= 500000:

Code:
n = 221628, 350071, 371696, 487291.
IMO any other 10^n+7 is composite.

The attached file should "prove" this assertion.
Attached Files
 10w7.PRPsearch.Proof.txt.7z (1.16 MB, 82 views)

2021-06-08, 09:33   #2
axn

Jun 2003

10100100100012 Posts

Quote:
 Originally Posted by Alfred IMO any other 10^n+7 is composite.
Do you mean "any other" in the specified range? Or n=[1..oo]?

 2021-06-08, 11:23 #3 Alfred     May 2013 Germany 3×29 Posts Any other in the specified range is meant.
2021-06-08, 11:48   #4
Dr Sardonicus

Feb 2017
Nowhere

10100110111102 Posts

Quote:
 Originally Posted by axn Do you mean "any other" in the specified range? Or n=[1..oo]?
I see the OP has answered graciously.

I would have been tempted to answer "Yes."

I point out If the attached file was supposed to prove that 10^n + 7 is composite for all other n, it would have been big news if it actually did that. (Especially since 10^n + 7 is prime for n = 1, 2, 4, 8, and 9).

A proof that 10^n + 7 is composite for all n greater than 5000000 would also be big news.

2021-09-22, 09:15   #5
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100101110101112 Posts

Quote:
 Originally Posted by Alfred I've found four probable primes in the range 200001 <= n <= 500000: Code: n = 221628, 350071, 371696, 487291. IMO any other 10^n+7 is composite. (up to this limit) The attached file should "prove" this assertion.
Makoto Kamada would be interested to extend his collection. https://stdkmd.net/nrr/1/10007.htm
Send those findings to him... and to OEIS: https://oeis.org/A088274

2021-09-27, 01:36   #6
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

986010 Posts

Quote:
 Originally Posted by axn Do you mean "any other" in the specified range? Or n=[1..oo]?
Buuuu! Are you a mersenne prime hunter or not?
(hint: 17, 107)

Last fiddled with by LaurV on 2021-09-27 at 01:42

2021-09-27, 01:41   #7
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

22·5·17·29 Posts

Quote:
 Originally Posted by Dr Sardonicus A proof that 10^n + 7 is composite for all n greater than 5000000 would also be big news.
That is most probably false, but if true, then that will be bad news...
(i mean, for us, like riesel, sierpinski, crus, gimps, etc, players)

2021-09-27, 03:23   #8
Dr Sardonicus

Feb 2017
Nowhere

2×2,671 Posts

Quote:
Originally Posted by LaurV
Quote:
 Originally Posted by Dr Sardonicus A proof that 10^n + 7 is composite for all n greater than 5000000 would also be big news.
That is most probably false, but if true, then that will be bad news...
(i mean, for us, like riesel, sierpinski, crus, gimps, etc, players)
I have no reason to doubt there are infinitely many primes of the form 10^n + 7. A proof that there are only finitely many, even that they've all been found - would certainly be disappointing to those looking for them. But if such a proof were found, imagine - just imagine - what a conceptual advance it would be!

Of course, a proof that there are infinitely many such primes would also represent an enormous conceptual advance, and would be much more satisfying all around.

 2021-09-27, 03:34 #9 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 227278 Posts Kamada's updated his site, I see. I updated OEIS.
2021-09-27, 03:41   #10
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

C7F16 Posts

Quote:
 Originally Posted by Dr Sardonicus I have no reason to doubt there are infinitely many primes of the form 10^n + 7. A proof that there are only finitely many, even that they've all been found - would certainly be disappointing to those looking for them. But if such a proof were found, imagine - just imagine - what a conceptual advance it would be! Of course, a proof that there are infinitely many such primes would also represent an enormous conceptual advance, and would be much more satisfying all around.
It is also conjectured that this is also true for every (a*b^n+c)/gcd(a+c,b-1) (a>=1, b>=2, c != 0, gcd(a,c) = 1, gcd(b,c) = 1) form which cannot be proven as only contain composites or only contain finitely many primes by using covering congruence, algebraic factorization, or combine of them (not only for 10^n+7, which is only the special case that (a,b,c) = (1,10,7)), contain infinitely many primes.

2021-09-27, 05:55   #11
Alfred

May 2013
Germany

3·29 Posts

Quote:
 Originally Posted by Batalov Kamada's updated his site, I see.
I informed Makoto Kamada.

Quote:
 Originally Posted by Batalov I updated OEIS.
Thank you.

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