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
abhishekrahul: 2017-01-19 13:52:25

enjoyed solving the problem ,very good question ,, it took some time ,, my 100th on spoj .............

code_aim: 2016-12-20 21:04:08

Very Good Question!!

vandan1177: 2016-11-13 16:02:32

Can someone please explain me the line - "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."

hpatel: 2016-08-22 21:44:03

Good application of BFS !

square1001: 2016-07-26 06:35:51

It is interesting, but I solved in 15-20 minutes :-)

baadshah_: 2016-07-15 21:52:08

AC in one GO!!nice problem
>>Nothing is "Impossible" << :P

manohar_4139: 2016-06-07 16:59:01

AC in one go..) nice problem

ajay_5097: 2016-05-26 16:11:07

My first on BFS !! Nice one :)

Last edit: 2016-05-26 16:11:36
hulk_baba: 2016-05-25 00:00:02

It's not necessary that the transitioning prime number lies between the 2 numbers, it may be greater. so be careful while bfs;

vijay kumar paliwal: 2016-05-23 13:32:11

M Lovin' It!

Added by:overwise
Time limit:0.845s
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