Improvising on the ideas of Wacław Sierpiński*, I found that infinitely many sequences of pairwise coprime octagonal numbers can be constructed, their first term a(1) being equal to any positive octagonal number and their general term being of the form a(n) = (k+1)*(3k+1), where k = Product_{i=1..n-1} a(i).
Any such sequence is infinite, which implies (by the Fundamental theorem of arithmetic) the infinitude of primes.
Example
One such sequence is 8, 225, 9727201, 919691230011613567201,...
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* see Problems 42 and 43 here, which involve triangular and tetrahedral numbers
Any such sequence is infinite, which implies (by the Fundamental theorem of arithmetic) the infinitude of primes.
Example
One such sequence is 8, 225, 9727201, 919691230011613567201,...
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* see Problems 42 and 43 here, which involve triangular and tetrahedral numbers
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