The Goldbach Conjecture states that every even number greater than 2 can be expressed as a sum of two primes.
For example, 4=2+2 and 16 = 5 + 11.
What is the smallest number for which there are 5 different ways to express this number as a sum of two primes?
(In reply to
computer solution (spoiler) by Charlie)
The first listing, of the first several numbers where the sum could be done in at least 5 ways, left out some ways, where the two primes in the sum are equal, such as 37+37 = 74, bringing that number's ways up to 5; likewise with 41+41 = 82. Corrected is:
48 5
5 43 7 41 11 37 17 31 19 29
54 5
7 47 11 43 13 41 17 37 23 31
60 6
7 53 13 47 17 43 19 41 23 37 29 31
64 5
3 61 5 59 11 53 17 47 23 41
66 6
5 61 7 59 13 53 19 47 23 43 29 37
70 5
3 67 11 59 17 53 23 47 29 41
72 6
5 67 11 61 13 59 19 53 29 43 31 41
74 5
3 71 7 67 13 61 31 43 37 37
76 5
3 73 5 71 17 59 23 53 29 47
78 7
5 73 7 71 11 67 17 61 19 59 31 47 37 41
82 5
3 79 11 71 23 59 29 53 41 41
84 8
5 79 11 73 13 71 17 67 23 61 31 53 37 47 41 43
86 5
3 83 7 79 13 73 19 67 43 43
90 9
7 83 11 79 17 73 19 71 23 67 29 61 31 59 37 53 43 47
94 5
5 89 11 83 23 71 41 53 47 47
96 7
7 89 13 83 17 79 23 73 29 67 37 59 43 53
100 6
3 97 11 89 17 83 29 71 41 59 47 53
102 8
5 97 13 89 19 83 23 79 29 73 31 71 41 61 43 59
104 5
3 101 7 97 31 73 37 67 43 61
106 6
3 103 5 101 17 89 23 83 47 59 53 53
108 8
5 103 7 101 11 97 19 89 29 79 37 71 41 67 47 61
110 6
3 107 7 103 13 97 31 79 37 73 43 67
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Posted by Charlie
on 2010-06-12 17:02:05 |
re: computer solution (spoiler)
