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Old 2021-06-08, 07:20   #1
Alfred
 
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Default 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
File Type: 7z 10w7.PRPsearch.Proof.txt.7z (1.16 MB, 53 views)
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Old 2021-06-08, 09:33   #2
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Quote:
Originally Posted by Alfred View Post
IMO any other 10^n+7 is composite.
Do you mean "any other" in the specified range? Or n=[1..oo]?
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Old 2021-06-08, 11:23   #3
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Any other in the specified range is meant.
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Old 2021-06-08, 11:48   #4
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Quote:
Originally Posted by axn View Post
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.
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Old 2021-09-22, 09:15   #5
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Quote:
Originally Posted by Alfred View Post
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
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Old 2021-09-27, 01:36   #6
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Quote:
Originally Posted by axn View Post
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
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Old 2021-09-27, 01:41   #7
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Quote:
Originally Posted by Dr Sardonicus View Post
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)
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Old 2021-09-27, 03:23   #8
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Quote:
Originally Posted by LaurV View Post
Quote:
Originally Posted by Dr Sardonicus View Post
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.
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Old 2021-09-27, 03:34   #9
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Kamada's updated his site, I see.
I updated OEIS.
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Old 2021-09-27, 03:41   #10
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Quote:
Originally Posted by Dr Sardonicus View Post
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.
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Old 2021-09-27, 05:55   #11
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Quote:
Originally Posted by Batalov View Post
Kamada's updated his site, I see.
I informed Makoto Kamada.

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