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<p>that every even number is the sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the <a href="page.php?w=Euclid-Euler_theorem">Euclid-Euler theorem</a>) that all even perfect numbers can be constructed from Mersenne primes. He introduced methods from <a href="page.php?w=mathematical_analysis">mathematical analysis</a> to this area in his proofs of the infinitude of the primes and the <a href="page.php?w=divergence_of_the_sum_of_the_reciprocals_of_the_primes">divergence of the sum of the reciprocals of the primes</a></p><p>
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