- #1
al-mahed
- 262
- 0
Every prime number > 3 could be written as a sum of a prime number and a power of two.
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
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