 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Samba Primes (Posted on 2011-06-14) 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?

 No Solution Yet Submitted by broll Rating: 3.6000 (5 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Hmmmm... computer solution (spoiler) | Comment 2 of 9 | When this puzzle was in the queue, I hadn't thought of the limitations on the 4-digit primes, and was given a solution by the poser, broll, but only perused is far enough to see that there were only 8 candidate 4-digit primes.  I didn't go through the remainder of the solution. But now that I've solved it myself, I see there are two solutions.

First the program and its findings:

`   5   dim Pr4(10)  10   N\$="7532":H\$=N\$:PCt=0  15   repeat  20    gosub *Permute(&N\$)  30    if prmdiv(val(N\$))=val(N\$) then inc PCt:print PCt;N\$:Pr4(PCt)=val(N\$)  35   until N\$=H\$ 100   for A=1 to PCt:for B=1 to PCt 110     Pr8=10000*Pr4(A)+Pr4(B) 120     if prmdiv(Pr8)=Pr8 then print Pr8;A;B 199   next B:next A 740   end 800`

The permute algorithm is listed elsewhere on the site.

` 1 2357 2 2753 3 3257 4 3527 5 5237 6 5273 7 7253 8 7523 23572753  1  2 23573527  1  4 23577523  1  8 27533257  2  3 32575273  3  6 35272357  4  1 52732357  6  1 52737253  6  7 72533257  7  3 72537523  7  8 75235273  8  6 `

First the 4-digit primes are numbered 1 to 8. Then the formable 8-digit primes are listed, with the numbers of the two 4-digit primes that make up each one.

Two possible sets of assignment work. I show the ordinal number of the 4-digit prime beneath the corresponding letter:

`CAPTURES     CAPTURES65713248     75316842`

In the first set, S equates to the 8th 4-digit prime, 7523. In the second set, S equates to the 2nd 4-digit prime, 2753.

 Posted by Charlie on 2011-06-14 14:46:24 Please log in:

 Search: Search body:
Forums (0)