## Symmetry In Prime Numbers

tags | Prime numbers | SymmetryLooking for symmetry in prime numbers does not necessarily mean "looking for symmetry IN prime numbers". Symmetry is found *between* them.

A hint of symmetry is displayed by the distance between them (the gap numbers)

Plotting consecutive gap numbers as a pair of coordinates reveals a symmetrical property:

A prime number is symmetrically surrounded by two other prime numbers only if their distance is a multiple of 6 (or the product of the first two prime numbers!)

∀(p, p+k, p + 2k), k=2×3×m, where m∈S={1/3,1,2,3,...,N}

Here are some examples (consecutive):

47, 53, 59

151, 157, 163

167, 173, 179

251, 257, 263

257, 263, 269

367, 373, 379

557, 563, 569

This integer sequence is present in the On-line Encyclopedia of Integers Sequences: A128940