

A113832


Triangle read by rows: row n (n>=2) gives a set of n primes with the property that the pairwise averages are all primes, having the smallest largest element.


8



3, 7, 3, 7, 19, 3, 11, 23, 71, 5, 29, 53, 89, 113, 3, 11, 83, 131, 251, 383, 5, 29, 113, 269, 353, 449, 509, 5, 17, 41, 101, 257, 521, 761, 881, 23, 431, 503, 683, 863, 1091, 1523, 1871, 2963, 31, 1123, 1471, 1723, 3463, 3571, 4651, 5563, 5743, 6991
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OFFSET

2,1


COMMENTS

If there is more than one set with the same smallest last element, choose the lexicographically earliest solution.
For distinct primes, the solution for n=5 is {5, 29, 53, 89, 173}.


REFERENCES

Antal Balog, The prime ktuplets conjecture on average, in "Analytic Number Theory" (eds. B. C. Berndt et al.) Birkhäuser, Boston, 1990, pp. 165204. [Background]


LINKS



EXAMPLE

Triangle begins:
3, 7
3, 7, 19
3, 11, 23, 71
5, 29, 53, 89, 113
3, 11, 83, 131, 251, 383
5, 29, 113, 269, 353, 449, 509
The set of primes generated by {5, 29, 53, 89, 113} is {17, 29, 41, 47, 59, 59, 71, 71, 83, 101}.


CROSSREFS

See A115631 for the case when all pairwise averages are distinct primes.


KEYWORD

nonn,tabf


AUTHOR



EXTENSIONS



STATUS

approved



