1583

This number is a prime.

This emirp with distinct digits is the largest prime factor of 25328, the number of emirps with distinct digits. [Capelle]

The smallest prime that is the sum of 3^3 consecutive primes: 1583 = 7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83+89+97+101+103+107+109+113. [Noll]

1583 is the smallest emirp such that the sum of each digit d raised to the power d is an emirp (1^1+5^5+8^8+3^3). [Silva]

The smallest emirp that is the sum of first n nontrivial (multidigit) palindromes (11+22+33+...+161+171=1583). [Bajpai]

The smallest Sophie Germain prime p such that sod(p); the sod(p^2); the sod(p^3); all are prime. [Bajpai]