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
rahulrawat09: 2019-12-04 17:22:43

evolution of comment section
2010: "Nice ques! BFS is the key here"
2019: "AC in one go"

parvezaalam786: 2019-11-23 16:56:04

first find all the 4 digit prime no. , make the adjacency list by adding the numbers if they differ by one digit and then do the bfs for getting the shortest path(minimum cost)

vamsi99: 2019-09-25 11:28:22

AC in one go

adrisos: 2019-08-17 12:25:08

Can someone pleeeeease comment some test cases?
I get SIGSEGV every time i send the code

Last edit: 2019-08-17 13:02:47
garry_555: 2019-08-13 22:26:29

nyc qs on BFS! use sieve for prime :D !! must do

sanket17: 2019-08-08 13:02:26

Last edit: 2019-08-08 13:02:37
cenation007: 2019-06-03 06:47:13

good question
just sieve and bfs
AC in one go :)

Last edit: 2019-06-03 06:48:21
shan61916: 2019-05-23 23:35:11

"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."
can be ignored.

jha_shashank: 2019-05-10 15:19:56

Nice problem:)
AC in one go!
Wondering if there were any impossible cases.

Jumpy: 2019-03-31 09:28:26

Nice question.
1) First get the list of primes.
2) Create a graph and
3) Do the dfs/bfs to find the answer.

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