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May 5th, 2016, 11:25 AM  #1 
Newbie Joined: Apr 2016 From: Canada Posts: 16 Thanks: 0  Primes to solve prime accuracy of +2
not sure if this is already known.. i just came up with this right now. x^2 + y^2 + 3^n where x = prime p y = next prime (p+1) n = order along the calculation / the nth pair of terms 2^2 + 3^2 + 3^0 = 14 (141=13) 3^2 + 5^2 + 3^1 = 37 5^2 + 7^2 + 3^2 = 83 7^2 + 11^2 + 3^3 = 197 11^2 + 13^2 + 3^4 = 371 (14+2=373) 13^2 + 17^2 + 3^5 = 701 17^2 + 19^2 + 3^6 = 1379 (1379+2=1381) 19^2 + 23^2 + 3^7 = 3077 (3077+2=3079) 41^2 + 43^2 + 3^12 = 534971 < prime number 
May 5th, 2016, 05:15 PM  #2 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 391 Thanks: 70 
Please explain further. I don't see the point of these calculations. Some of the results are prime and some are not. 
May 6th, 2016, 04:40 PM  #3 
Newbie Joined: Apr 2016 From: Canada Posts: 16 Thanks: 0 
if this has an accuracy of + 2, it'sstill viable.. similar to how Mersenne prime are valid.. right? also, i wonder if the + 2 is because of the 3... also i haven't thoroughly tested this for absolutely all available primes but what i have done seems to show a pattern of a + accuracy of 2 
May 6th, 2016, 06:37 PM  #4 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 391 Thanks: 70 
Thanks Kensou. At first I didn't understand that you were saying that the resultant number is either a prime or within + or 2 of a prime. I think I may have found a counterexample with the twin primes 101 and 103. Please check these calculations: 101^2 = 10201 103^2 = 10609 3^24 = 282,429,536,481 The sum of these three results is 282,429,557,291 which is not prime. Neither is 282,429,557,289 nor 282,429,557,293. 
May 6th, 2016, 08:16 PM  #5  
Newbie Joined: Apr 2016 From: Canada Posts: 16 Thanks: 0  Quote:
 

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