20181219, 10:59  #122 
Mar 2018
17×31 Posts 
...continue...
moreover pg(36) is prime
pg(36*1935=69660) is prime...36+1=37 is prime...69660+1=69661 is prime 
20181219, 13:01  #123  
Feb 2017
Nowhere
2^{5}·139 Posts 
Quote:
10^2 = 85 + 15 == 2 (mod 17), so 10^8 = (10^2)^4 == 1 (mod 17), so that 10^9 == 10 (mod 17), giving 10^9  7 == 0 (mod 17). Last fiddled with by Dr Sardonicus on 20181219 at 13:01 

20181219, 14:24  #124 
Mar 2018
17·31 Posts 
pg(56238) and pg(75894)
pg(56238) and pg(75894) are prp
56238 and 75894 are multiples of 546. when pg(13k) is prime, then 13k is also a multiple of 42 
20181219, 15:19  #125  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:


20181220, 05:19  #126  
Aug 2006
13541_{8} Posts 
Quote:


20181220, 05:46  #127 
Jun 2003
13^{2}×29 Posts 

20181220, 09:41  #128 
Mar 2018
1000001111_{2} Posts 
exponents leading to a prime
pg(51456), pg(56238), pg(69660) and pg(75894) are three consecutive pg primes.
51456, 56238, 69660 and 75894 are multiples of 6. Moreover pg(3336), pg(51456), pg(56238), pg(69660) and pg(75894) are primes and 3336, 51456, 56238, 69660, 75894 are divisible by a prime of the form 6s+1 
20181220, 11:06  #129 
Mar 2018
17×31 Posts 
pg(19) and pg(285019) are probable primes, the only ones with 19 and 285019 multiples of 19.
19 and 285019 end with digits 19 
20181220, 11:21  #130 
Mar 2018
17·31 Posts 
pg(19k)
pg(19k) is prime only when 19k is congruent to 19 mod 10

20181220, 16:18  #131 
Feb 2017
Nowhere
2^{5}·139 Posts 
Hmm. The 2 values of 19*k have k = 1 and k = 15001. So, all (two) PRP values of pg(19*k) (found so far) have 19*k congruent to 19 (mod 15000), or k == 1 (mod 15000).
But wait  there's more!!! That second value of k is 15001 = 7*2143. Now, everyone knows that 22/7 is a good approximation to the number pi  it's a convergent to the simple continued fraction for pi. Less well known is that, as discovered by Ramanujan, (2143/22)^(1/4) is quite a good approximation to pi, good to 8 decimal places! And there are both 7 and 2143 in that second kvalue! What does it all mean?!? 
20181220, 16:29  #132 
"Forget I exist"
Jul 2009
Dumbassville
20300_{8} Posts 

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