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A362778
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Triangular array read by rows: T(n,k) is the least prime factor of n!*k + 1, n >= 1, 1 <= k <= n.
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2
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2, 3, 5, 7, 13, 19, 5, 7, 73, 97, 11, 241, 19, 13, 601, 7, 11, 2161, 43, 13, 29, 71, 17, 15121, 20161, 11, 30241, 35281, 61, 11, 73, 161281, 449, 241921, 282241, 47, 19, 293, 1088641, 1451521, 23, 2177281, 13, 2903041, 17, 11, 13, 10886401, 233, 18144001, 17, 101, 29030401, 32659201, 43
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OFFSET
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1,1
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COMMENTS
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The primes in each row are distinct because n!*k + 1 are coprime for 1 <= k <= n, and hence this array gives a simple proof that there are infinitely many prime numbers.
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LINKS
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FORMULA
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EXAMPLE
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Triangle T(n,k) begins:
n\k 1 2 3 4 5 6 ...
1 2
2 3 5
3 7 13 19
4 5 7 73 97
5 11 241 19 13 601
6 7 11 2161 43 13 29
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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