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
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.

sourav01: 2019-03-10 14:40:01

awesome problem_/\_

kuchnahiaata: 2019-03-02 09:25:40

the real stuff lies in the construction of graph rest is just bfs!! but awesome problem _/\_

vickyand_27: 2019-01-30 18:45:36

In bfs who have to maintain a distnce array :)) MY 12

xtmosphere: 2019-01-15 19:55:45

Im(Its)-Possible :D
Nice problem ..

sonuexpc: 2018-12-28 20:19:12

good problem for beginners...my first bfs accepted in 1 go :)

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

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