Burt Kaliski Jr. (@modulomathy)
3/9/12 7:52 AM
#math trivia for #March9: #69 can be expressed as the sum of three primes many ways, incl. 23+23+23. What are the other ways?
The primes must all be odd, because 2+2 would have to be added to 65, which is not prime.
The largest of the primes must be at least 23, so let’s start with that and enumerate the possibilities for the others, which must be the same or smaller:
- 23+46: 46 = 23+23
- 29+40: 40 = 23+17
- 31+38: 38 = 19+19, 31+7
- 37+32: 32 = 19+13, 29+3
- 41+28: 28 = 17+11, 23+5
- 43+26: 26 = 13+13, 19+7, 23+3
- 47+22: 22 = 11+11, 17+5, 19+3
- 53+16: 16 = 11+5, 13+3
- 59+10: 10 = 5+5, 7+3
- 61+8: 8 = 5+3
- 67+1: no answers
All together, this is 19 combinations, including the one given in the problem statement.
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