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In Unsolved Problems in Number Theory, 3rd edition, section D1, 2004, R. K. Guy says, "Andrew Bremner has computed the rational rank of the elliptic curve x^3 + y^3 = Taxicab(n) as equal to 2, 4, 5, 4 for n = 2, 3, 4, 5, respectively." But Taxicab(n) equals A011541(n), not the cubefree taxicab number A080642(n). @Lucia
In a 1978 interview in "Pour la Science" Weil said, "Or l’hypothèse de Riemann n’est pas un point isolé des mathématiques, mais au contraire, constitue un verrou de la théorie des nombres. Pour la démontrer, il faudrait d’abord mieux connaître, et par conséquent faire progresser la théorie des nombres." This is quoted by Michèle Audin on p. 666 of her book "Correspondance entre Henri Cartan et André Weil (1928-1991)", Société mathématique de France, 2011, available at ams.org/bookstore-getitem/item=SMFDM-6 for purchase.
Geoffrey Caveney has pointed out a related statement by Brian Conrey: It is my belief that RH is a genuinely arithmetic question that likely will not succumb to methods of analysis." See the last paragraph of his article The Riemann Hypothesis'' in the March 2003 AMS Notices, available at ams.org/notices/200303/fea-conrey-web.pdf
The URL is ami.ektf.hu/uploads/papers/finalpdf/AMI_37_from151to164.pdf for our paper D. Marques and J. Sondow, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164.
Although the title of Weil's paper includes ``nombres premiers,'' the quoted reviews of his and Burnol's papers do not mention primes. So we still have no example of a quotation that explicitly links Weil to both the Riemann Hypothesis and prime numbers.
