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2020-02-17, 22:01
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#1 |
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Mar 2018
2·5·53 Posts |
Primes of the form 555... 915824341
555915824341 is prime
No other prime found of the form 555...5915824341. Curiously the Wieferich prime 1093 divides 55555555555555555555555555555555915824341 |
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2020-02-17, 22:17
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#2 |
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Jan 2017
3·11 Posts |
Certainly a low-weight sequence, but 5*(10^156-1)/9+360268786 is prime.
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2020-02-17, 22:23
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#3 |
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Mar 2018
2·5·53 Posts |
...
Finitely many?
555915824341 is a quadratic residue mod 1093 Last fiddled with by enzocreti on 2020-02-17 at 23:04 |
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2020-02-18, 00:21
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#4 |
Feb 2017
Nowhere
4,643 Posts |
I checked the number of leading 5's out to 2000. Four of them gave (pseudo)primes.
Code:
? k=915824341;for(i=1,2000,k*=10;k-=3242419069;if(ispseudoprime(k),print(i))) 3 147 179 1643 1, 4, 7, ... 3*k + 1 leading 5's the number is divisible by 3 2, 8, 14, ... 6*k + 2 leading 5's the number is divisible by 13 so half the numbers are divisible either by 3 or 13. |
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2020-02-18, 10:28
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#5 |
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Mar 2018
2·5·53 Posts |
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yes I noted that too
I think that there is an explanation for that |
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2020-02-18, 11:30
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#6 |
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Mar 2018
2×5×53 Posts |
Proof
can be given a proof that when the number is divisible by 557, then it is also divisible by 19 and by 13?
5*(10^59-1)/9+360268786 for example is divisible by 557 and by 19 and 13 and a proof that when the number is divisible by 1093 is divisible also by 19 and by 13? Last fiddled with by enzocreti on 2020-02-18 at 11:35 |
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2020-02-18, 12:15
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#7 |
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Mar 2018
2×5×53 Posts |
primes of the form 8n+5
maybe when the numer has a small factor as 557 or 1093 (primes of the form 8n+5), then it is also divisible by 13 and 19?
so for example 5*(10^23-1)/9+360268786 is divisible by 13, 19 and 29 (prime of the form 8n+5) Last fiddled with by enzocreti on 2020-02-18 at 12:18 |
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2020-02-18, 19:34
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#8 | ||
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Feb 2017
Nowhere
4,643 Posts |
Quote:
Quote:
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