Prime Curios!: 312

312
(another Prime Pages' Curiosity)

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312 is the only number m less than 30000 such that prime(k*m) + k*m is prime for k = 1, 11, 1111, 111111, 11111111, and 111111111. [Firoozbakht]

312 is the smallest number m such that prime(1111*m) + 1111*m, and prime(1111*m) - 1111*m are primes. [Firoozbakht]

312 = prime(3*1*2) * phi(3*1*2) * sigma(3*1*2). It is the only known number with this property (up to 10^8). [Firoozbakht]

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