Any even number greater than or equal to 4 can be written as the sum of two primes.

Is this conjecture true if we replace "even" by "odd"?

Is this conjecture true if we replace "sum" by "product"?

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- Sep 28th 2010, 09:15 PMMATNTRNGGoldbach Conjecture
Any even number greater than or equal to 4 can be written as the sum of two primes.

Is this conjecture true if we replace "even" by "odd"?

Is this conjecture true if we replace "sum" by "product"? - Sep 28th 2010, 10:01 PMundefined
Since 2 is the only even prime, we get the first counterexample when we have two composite odd numbers in a row... namely, 27.

For the second question just take 2*3*5 as counterexample... or 2*2*2 for that matter.

EDIT: Actually the first counterexample for the "odd" problem is 11, I wasn't thinking clearly when I wrote 27. (27 is the smallest odd number greater than 4 that cannot be written as the sum of*at most*2 primes.)