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?
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.
P= 5273 <br>
So S IS left unassigned with only one fourtuple left i.e 2753<br>
Truly beautiful & surprising problem. Like!!
Edited on June 14, 2011, 7:51 pm