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Programming Enigma Puzzles

5 April 2019

Posted by on **From New Scientist #2172, 6th February 1999** [link]

A semi-prime is the product of two prime numbers. Sometimes when the digits of a semi-prime are reversed, the resulting number is also a semi-prime: 326 and 623 (2 × 163 and 7 × 89 respectively) are both semi-primes. More rarely the sum of these two semi-primes is itself a semi-prime, as with 326 + 623 = 949 = 13 × 73.

In fact, 949 is the largest of very few three-digit semi-primes that have these characteristics; but two of the three-digit semi-primes that can be the sum of two semi-primes, of which one is the reverse of the other, are consecutive numbers.

Identify these two consecutive three-digit numbers and the sums that lead to them. (Give your answer in the form

a = b + candd = e + f, whered = a + 1).

[enigma1016]

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This Python program runs in 100ms.

Run:[ @repl.it ]Solution:The consecutive numbers are 706 (= 155 + 551) and 707 (=205 + 502).The prime factorisations of these numbers are:

The full list of semi-prime sums are: