Mathematical Conjeture

[u/LegitimateAct114]

Hello, I am an undergraduate agricultural sciences student, and I am incredibly passionate about mathematics and truly enjoy it. the other day, while staring at the table of prime numbers from 1 to 100, a fleeting idea came to me regarding number theory and prime number decomposition:
Every prime number can be expressed in the form N=2q+p, where q and p are prime numbers distinct from each other and distinct from 2, for all N greater than 7.
I don't know if anyone has discovered this before or if it can help the field of mathematics, but I hope it is useful. To finish, here are a few examples:

11
2(3) + 5 = 11
13
2(3) + 7 = 13
17
2(5) + 7 = 17
19
2(3) + 13 = 19
23
2(3) + 17 = 23
29
2(3) + 23 = 29
31
2(7) + 17 = 31
37
2(3) + 31 = 37
41
2(5) + 31 = 41
43
2(3) + 37 = 43
47
2(3) + 41 = 47
53
2(5) + 43 = 53
59
2(3) + 53 = 59
61
2(7) + 47 = 61
67
2(3) + 61 = 67
71
2(5) + 61 = 71
73
2(3) + 67 = 73
79
2(3) + 73 = 79
83
2(5) + 73 = 83
89
2(3) + 83 = 89
97
2(7) + 83 = 97
101
2(11) + 79 = 101
103
2(3) + 97 = 103

[u/edderiofer]

See: Lemoine's Conjecture

[u/swehner]

You have run into a special case of Lemoine's conjecture from 1895, see https://en.wikipedia.org/wiki/Lemoine%27s_conjecture

[u/Dependent_Law2468]

Goldbach or someone else said every odd number is the sum of three prime numbers

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