OFFSET
1,1
COMMENTS
Let Z be a sum of 36 consecutive primes. A necessary condition to get a 6 X 6 magic square using these primes is that Z=6S, where S is even. The smallest magic constant of a 6 X 6 magic square of consecutive primes is 484 (cf. A073520).
Each of the first 100 possible arrays of 36 consecutive primes which satisfy the necessary condition produces a magic square.
A program written by Stefano Tognon was used.
LINKS
Natalya Makarova, Author's webpage (in Russian)
FORMULA
EXAMPLE
S = 744
[139 113 151 131 83 127]
[223 149 89 47 157 79]
[173 103 181 167 59 61]
[ 67 137 53 97 211 179]
[101 199 73 109 71 191]
[ 41 43 197 193 163 107]
S = 806
[131 53 107 157 191 167]
[ 89 229 179 97 109 103]
[ 83 211 71 139 79 223]
[113 101 137 181 227 47]
[197 61 163 59 127 199]
[193 151 149 173 73 67]
S = 868
[191 137 79 193 197 71]
[ 67 157 73 229 239 103]
[179 173 167 97 101 151]
[211 181 223 61 109 83]
[113 131 199 139 59 227]
[107 89 127 149 163 233]
Magic square with S=930 can be pan-diagonal (cf. A073523).
Example of a non-pan-diagonal square:
S = 930
[167 71 151 199 131 211]
[ 89 241 181 73 113 233]
[ 83 227 127 197 229 67]
[239 137 139 103 163 149]
[179 97 223 251 101 79]
[173 157 109 107 193 191]
PROG
(PARI) A177434(n, p=A272387[n], N=6)=sum(i=2, N^2, p=nextprime(p+1), p)/N \\ Uses a precomputed array A272387, but can actually be used to find the terms, cf A272387. - M. F. Hasler, Oct 28 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Natalia Makarova, May 08 2010
EXTENSIONS
Edited by M. F. Hasler, Oct 28 2018
STATUS
approved