Every prime number > 3 could be written as a sum of a prime number and a power of two.(adsbygoogle = window.adsbygoogle || []).push({});

p,q are primes, n is positive whole number ==> p = q + 2^n

5 = 3 + 2^1

7 = 5 + 2^1 = 3 + 2^2

11 = 7 + 2^2

13 = 5 + 2^3

17 = 13 + 2^2

19 = 3 + 2^4

23 = 7 + 2^4

29 = 13 + 2^4

31 = 23 + 2^3

37 = 29 + 2^3

87 = 23 + 2^6

101 = 37 + 2^6

1213 = 701 + 2^9

1217 = 1153 + 2^6

1223 = 967 + 2^8

seems that this is really truth, but fails for some primes (997, 6659 are some primes that this is not true)

I wonder if there is some property which could be used to discriminate such primes

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# I made the following conjecture

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