The number of positive integers n for which 2n + 1, 4n + 7 and 8n + 3 are all primes is

• all the numbers must be prime so by heat and trial method by putting n=1 we get,
  2(1)+1=3,which is prime.
  4(1)+7=11,which is prime.
  8(1)+3=11,which is prime.
  so n=1.
  
• 11 years agoHelpfull: Yes(1) No(0)
• 1
  
  When n = 1 => (2n + 1, 4n + 7 and 8n + 3) = (3 , 11 , 11)
• 11 years agoHelpfull: Yes(0) No(1)
• If n = 1,2,3,4,...
  
  2n + 1 => 3 , 5 , 7 , 9, ...
  4n + 7 => 11, 15, 19, 23 ...
  8n + 3 => 11, 19, 27, 35 ...
  
  Only first column is prime number.
  For n = any value , atleast one is divisible by 3.
  
• 11 years agoHelpfull: Yes(0) No(1)