# Combinatorial prime puzzle

Is it true that no prime larger than $241$ can be made by either acting or subtracting $2$ coprime numbers made up out of the prime factors $2,3,$ and $5?$

# Update

Above example is clearly wrong, as shown by MJD. New question:Is it true that $251$ cannot be made by either acting or subtracting $2$ coprime numbers made up out of the prime factors $2,3,$ and $5?$

• Is $1$ allowed as one of the coprime numbers? – Mark Bennet Oct 31 '14 at 14:32
• @MarkBennet No ;) – martin Oct 31 '14 at 14:34
• What is the basis for your claim? – Ali Caglayan Oct 31 '14 at 14:37
• $251 = 256 -5 = 8 +243$. – MJD Oct 31 '14 at 14:51
• As far as I can tell that is true. – MJD Oct 31 '14 at 15:27

You mean like $162 + 625 = 787$?
Brute-force computer search finds many counterexamples; for example $2^{19} + 3^4 =524369$. If you are interested in this kind of conjecture, learning a minimal amount of computer programming would be a good investment of your time.
• Also $1039, 2063, 4111, 32783, 65551$ of the form $2^n+15$ – Mark Bennet Oct 31 '14 at 14:50