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# 739

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 smallest prime (emirp) that can be expressed as a sum of powers with the four prime digits as bases and exponents, i.e., (2^7+3^5+5^2+7^3). [Loungrides]

The smallest emirp that has a maximum product of digits for a prime sum of digits. [Loungrides]

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]

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 are 3 curios for this number that have not yet been approved by an editor.)
Printed from the PrimePages <primes.utm.edu> © G. L. Honaker and Chris K. Caldwell
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