Problems & Puzzles: Puzzles

Conjecture 88. Special Goldbach Partitions

Ivan Ianakiev sent the following nice conjecture

"Let p denote any prime in any decomposition of 2n. 4 and 6 are the only numbers n such that 2n + p is prime for every p". See OEIS A045917.

Known examples:


8=3+5; then 8+3 & 8+5 are primes.

12=5+7; then 12+5 &12+7 are primes.


Q. Can you find another example or prove the conjecture?


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