Prime Curios!: 512

512
(another Prime Pages' Curiosity)

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512 is the smallest (and only known) cube such that 512*2^512-1 is prime. [Gupta]

512 = 2^9. Both 2^9 +/- 9^2 are prime. This is the smallest number of the form 2^n such that both 2^n +/- n^2 are prime. [Astle]

(512 + 1)⁵¹² + 1 is an even semiprime. Note that 512 = 2 to the ninth power. [Wesolowski]

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