# 739

This number is a prime. The first Human Genome Project online download contained a 739 megabyte file. The smallest prime number that is the sum of distinct primes beginning and ending with the digit three (739 = 3 + 353 + 383). [Capelle] The only 3-digit prime (emirp) that remains prime when its leading digit is replaced by any digit that is equal to a power of 2, i.e., 1, 2, 4, 8. [Loungrides] The smallest emirp that has a maximum product of digits for a prime sum of digits. [Loungrides] (73*9) + (7*39) +/- 739 produces two prime numbers. [Homewood] The start of five consecutive emirps in the sequence of Ulam primes, i.e., 739, 751, 983, 991, 1103. [Loungrides] The smallest prime number that has both no digits in common with its square and the same sum of digits as its square. [Gaydos] The number of the 8-star Odin in Tower of Saviors. [Luen] 7^39 is a 33-digit number without a 7 in it. Can you find a larger power of 7 without the digit 7 in it? [Loungrides] 739 is the largest prime used in Jean Brette's 31-digit approximation for π: ln[(2^5*5#*23*29)^3+739+5]/sqrt(163) = 3.141592653589793238462643383279... . [Rivera] 739 is at the end of a conveyor belt on the cover of "The Prime Number Conspiracy: Biggest Ideas in Math from Quanta."

(There is one curio for this number that has not yet been approved by an editor.)