Template:Sequence of the Day for May 16

Intended for: May 16, 2013

Timetable

• First draft entered by Alonso del Arte on March 21, 2012 ✓
• Draft reviewed by Daniel Forgues on May 13, 2012 ✓
• Draft to be approved by April 16, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A077914: Numbers which can be expressed as the sum of two distinct primes in exactly two ways.

{ 16, 18, 20, 22, 26, 28, 32, 62, 68, ¿ ... ? }

Here we have another sequence believed to be finite and given in full, but we have no proof that 68 is the final term or at least that the sequence is finite. This question is related to the Goldbach conjecture thus: it appears that for most larger even numbers, there are a lot more than two ways to express them as a sum of distinct primes. For example, 70 = 67 + 3 = 59 + 11 = 53 + 17 = 47 + 23 = 41 + 29.