Let capitalised letters of the alphabet stand for 4-digit prime numbers each of whose digits is distinct and also prime, so that e.g. A=5237.

A pair of such letters stands for the concatenation of two such numbers to form an 8-digit number, e.g. AA=52375237

Denote 8 different such 4-digit primes by the letters of the word CAPTURES, so that each of CP,ET,PU,RU,TE,TR, and UC is also prime.

Given that A=5237, what is the value of S?

answer: S=2753

S o l u t i o n :

the choices for letters are: 2357,2753,3257,3527,**5237**,5273,7253,7523.<br>

**5237 is A, so we try pairs-combinations out of the remaining 7 four digits numbers.**

Using a prime/composite applet 8 eight digit numbers qualify, only two of them 23573522 & 35222357 fit the TE-ET **format**.

CAPTURES==><br>

C=3257<br>

A= **5237(KNOWN)**<br>

P= 5273 <br>

T= 2357<br>

U=7253<br>

R=7523<br>

E=3527<br>

**So S IS left unassigned with only one fourtuple left i.e 2753**<br>

**s=2753 **

**Truly beautiful & surprising problem. Like!!**

*Edited on ***June 14, 2011, 7:51 pm**