20200330, 11:52  #1 
Mar 2018
1F0_{16} 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 2^696601  2^695591 is prime 2^920201  2^920191 is prime!!! Last fiddled with by enzocreti on 20200330 at 11:53 
20200330, 12:19  #2 
Romulan Interpreter
Jun 2011
Thailand
8,543 Posts 
please show us a proof that they are prime

20200330, 12:50  #3 
Mar 2018
1F0_{16} Posts 
...
Well...
actually they are only probable primes... maybe in future they will be proven primes Last fiddled with by enzocreti on 20200330 at 12:52 
20200330, 17:39  #4 
Mar 2018
1F0_{16} Posts 
http://factordb.com/index.php?id=1100000001110801143 http://factordb.com/index.php?query=...%2B2%5E920191 Last fiddled with by enzocreti on 20200330 at 17:55 
20200330, 23:06  #5 
Mar 2018
496_{10} Posts 
... I note also...
I note also that
(lcm(215,344,559))^2=4999*10^5+6966060 I note that the polynomial X^2X*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 429^44*7967780460 which is a perfect square and lcm(215,344,559) divides 429^44*79677804601 Last fiddled with by enzocreti on 20200401 at 08:07 
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