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
shivansh100: 2018-12-03 16:04:08

test files are weak :((

kumar18tushar: 2018-11-30 08:05:29

50th ;
0.00 27M

Last edit: 2018-11-30 08:05:56
manishjoshi394: 2018-11-21 08:56:55

Awesome problem, got AC in first try. Took an hour to code it :(

salman3007: 2018-09-27 10:44:37

AC in a go. bfs +implementation

jagadishsagi: 2018-09-21 04:49:00

Nice problem easy bfs AC with 0.01s

saketag007: 2018-09-11 10:56:25

easy bfs 0.07

tanardi gunawan: 2018-08-31 08:27:47

easy problem using string ac in 0,19s!!!

masterchef2209: 2018-08-24 13:11:26

Pretty Straightforward problem
wasted 3 hours trying different implementation for calculating shortest distance but error was in logic to check 'one digit difference' between prime numbers; *ultimate facepalm moment*
but still AC in 1 go :P

shivan11: 2018-07-26 18:36:20

Good bfs problem. Store the sieve of prime numbers beforehand so you dont have to calculate all the prime numbers for every test case.

kkislay20: 2018-06-30 08:26:10

OMG this problem...I don't know about you guys but this was a really nice problem. The bfs,graph,sieve and concept was really good. I was getting WA even though all my answers were correct but there was one testcase which was not giving correct ans...I dont know why, After hitting walls for few hours I replaced the memset with loop and got AC.If you want to know the test case..this was the one-
4241 6101
5099 7159
1559 9437
Correct ans- 5 5 4
My ans was- 5 5 5
And lastly I though I will be getting TLE but we have big enough time space.

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