PPATH - Prime Path

The ministers of the cabinet were quite upset by the message from the Chief of Security stating that they would all have to change the four-digit room numbers on their offices.
— It is a matter of security to change such things every now and then, to keep the enemy in the dark.
— But look, I have chosen my number 1033 for good reasons. I am the Prime minister, you know!
— I know, so therefore your new number 8179 is also a prime. You will just have to paste four new digits over the four old ones on your office door.
— No, it's not that simple. Suppose that I change the first digit to an 8, then the number will read 8033 which is not a prime!
— I see, being the prime minister you cannot stand having a non-prime number on your door even for a few seconds.
— Correct! So I must invent a scheme for going from 1033 to 8179 by a path of prime numbers where only one digit is changed from one prime to the next prime.

Now, the minister of finance, who had been eavesdropping, intervened.
— No unnecessary expenditure, please! I happen to know that the price of a digit is one pound.
— Hmm, in that case I need a computer program to minimize the cost. You don't know some very cheap software gurus, do you?
— In fact, I do. You see, there is this programming contest going on...

Help the prime minister to find the cheapest prime path between any two given four-digit primes! The first digit must be nonzero, of course. Here is a solution in the case above.

The cost of this solution is 6 pounds. Note that the digit 1 which got pasted over in step 2 can not be reused in the last step – a new 1 must be purchased.


One line with a positive number: the number of test cases (at most 100). Then for each test case, one line with two numbers separated by a blank. Both numbers are four-digit primes (without leading zeros).


One line for each case, either with a number stating the minimal cost or containing the word Impossible.


1033 8179
1373 8017
1033 1033


hide comments
Shubham Bansal: 2015-03-29 14:20:18

a very nice problem...

pandu ranga rao: 2015-03-06 21:36:40

Nice QN..!

Anubhav Gupta: 2015-02-11 21:46:28

Awesome question!!

epsilon: 2015-01-24 12:01:02

my 50th on spoj...........till now it's
best question i had ever sloved!!!!!!!!!

fanatique: 2015-01-08 14:42:37

good one... :)

Mitch Schwartz: 2015-01-02 08:55:39

"Piece of Cake!! Simple [hint] it is!!! Skilled implementation is the key though :P"

Here we see clearly one of the main reasons people keep leaving spoilers in comments: to brag.

Another reason could be that they dislike thinking so much that they consider it a kindness to save other people from the hassle.

Last edit: 2015-01-02 11:33:33
Swapnil Borse: 2015-01-02 08:49:38

Piece of Cake!! Simple BFS it is!!! Skilled implementation is the key though :P

agaurav77: 2014-12-27 16:36:21

This one is a super awesome one. Those who don't get how to start, here's a hint : Think of Dijkstra !

AC :)

Gaurav Bansal: 2014-12-24 08:14:36

these type of questions illustrates why programming is awesome!!

yagyank: 2014-11-29 22:05:17

weak test cases!!!

Added by:overwise
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM ICPC NWERC 2006