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We consider the representation of primes as a sum of a prime and twice atriangular number. We prove that a subset of the primes having density 1 isexpressible in this form. We conjecture that every odd prime number isexpressible as a sum of a twin prime and twice a triangular number. We showthat this conjecture implies the existence of infinitely many twin primes.

Primes of the form n^2+n+p have density 1