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 2019-04-10, 14:17 #1 enzocreti   Mar 2018 2×263 Posts for which values of p this expression has the form s*2^k? let be p an arbitrary prime... can you find values of p such that (10^p-1)/9+1 has the form s*2^k? where s is a prime and k an integer >0 example p=3 does the job infact (10^3-1)/9+1 has the form 7*2^4 p=5 does not the job because (10^5-1)/9+1 has the form 2^3*3*463...
 2019-04-10, 14:57 #2 enzocreti   Mar 2018 2·263 Posts Primes that do the job up to 103 I found that the primes that do the job up to p=103 are: 3, 7, 43. Is there some relation with the fact that 10^r+333667 is prime for r=3,7 and 43 and no other prime r up to r=26.000? Last fiddled with by enzocreti on 2019-04-10 at 15:06
2019-04-11, 01:14   #3
wblipp

"William"
May 2003
New Haven

2·32·131 Posts

Quote:
 Originally Posted by enzocreti let be p an arbitrary prime... can you find values of p such that (10^p-1)/9+1 has the form s*2^k?
2, 3, 7, 229, 1579

 2019-04-11, 14:01 #4 Dr Sardonicus     Feb 2017 Nowhere 3×5×233 Posts I note that if n > 3 then N = ((10^n - 1)/9 + 1)/8 is an odd integer. Also, n need not be prime for N to be prime. Code: ? for(i=4,1000,n=1+(10^i-1)/9;n=n/8;if(ispseudoprime(n),print(i))) 4 7 16 43 58 106 160 229 628

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