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May 5th, 2016, 12:25 PM   #1
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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 (14-1=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
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May 5th, 2016, 06:15 PM   #2
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Please explain further. I don't see the point of these calculations.
Some of the results are prime and some are not.
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May 6th, 2016, 05:40 PM   #3
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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
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May 6th, 2016, 07:37 PM   #4
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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 counter-example 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.
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May 6th, 2016, 09:16 PM   #5
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Quote:
Originally Posted by Timios View Post
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 counter-example 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.
any idea what the nearest + and - primes are to that result?
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