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
shubham2912: 2021-10-16 14:05:03

AC in one go..bfs on graph, but i forgot toconsider case for IMPOSSIBLE and instead printed-1 but still AC

darkcry_69: 2021-07-19 14:33:48

I believe the time complexity of intended solution using bfs is O( (no of primes between 1000 and 9999) * 10000).
Tell me if I am wrong.

mani_jo: 2021-06-26 14:54:53

i got RE again and again

kritak: 2021-05-19 06:37:25

8019 is not a prime number. Both the numbers should be prime as mentioned in the problem.

aman_kumar_97: 2021-04-02 18:52:51

I forgot to include the impossible case and still, my solution worked xD
There is no impossible test case :)

csdeshpande19: 2021-02-23 19:43:18

Try this case:
1033 8019
1373 8017
1033 1033

O/P -

amdee07: 2020-12-31 17:14:39

AC in one go.. great use of graph

ritikagarwal47: 2020-10-23 17:24:28

Best Problem

yogi23: 2020-10-07 22:27:11

interesting one ;)

paawan9s: 2020-10-07 18:08:38

ac in one go!!!

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