"Goldbach Conjectures", by Randall Munroe, licensed under Creative Commons Attribution-NonCommercial 2.5 License

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The weak twin primes conjecture states that there are infinitely many pairs of primes. The strong twin primes conjecture states that every prime p has a twin prime (p+2), although (p+2) may not look prime at first. The tautological prime conjecture states that the tautological prime conjecture is true.