mersenneforum.org 69660 and 92020
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 2020-03-30, 11:52 #1 enzocreti   Mar 2018 1F016 Posts 69660 and 92020 69660 and 92020 are multiple of 215 and congruent to 344 mod 559 92020=lcm(215,344,559)+69660 | denotes concatenation in base 10 2^69660-1 | 2^69559-1 is prime 2^92020-1 | 2^92019-1 is prime!!! Last fiddled with by enzocreti on 2020-03-30 at 11:53
 2020-03-30, 12:19 #2 LaurV Romulan Interpreter     Jun 2011 Thailand 205448 Posts please show us a proof that they are prime
 2020-03-30, 12:50 #3 enzocreti   Mar 2018 1111100002 Posts ... Well... actually they are only probable primes... maybe in future they will be proven primes Last fiddled with by enzocreti on 2020-03-30 at 12:52
2020-03-30, 17:39   #4
enzocreti

Mar 2018

1111100002 Posts

Quote:
 Originally Posted by LaurV please show us a proof that they are prime

http://factordb.com/index.php?id=1100000001110801143

http://factordb.com/index.php?query=...%2B2%5E92019-1

Last fiddled with by enzocreti on 2020-03-30 at 17:55

 2020-03-30, 23:06 #5 enzocreti   Mar 2018 24×31 Posts ... I note also... I note also that (lcm(215,344,559))^2=4999*10^5+69660-60 I note that the polynomial X^2-X*429^2+7967780460=0 has the solution x=69660 If you see the discriminant of such polynomial you can see interesting things about pg primes with exponent multiple of 43 I note that 429^2 is congruent to 1 mod 215 and to 1 mod 344. I note that 92020*2+1=429^2 The discriminant of the polynomial is 429^4-4*7967780460 which is a perfect square and lcm(215,344,559) divides 429^4-4*7967780460-1 Last fiddled with by enzocreti on 2020-04-01 at 08:07

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