An unknown route with a MAP invites an INROAD from many an IMP.

Now **MAP * IMP = INROAD** if the following conditions are met:

1. The two multipliers are semiprimes.

2. Each of the 4-digit partial products are a pair of consecutive integers with a difference equal to their multiplying digit.

Determine the 4 primes which form the original multipliers.

__Bonus Challenge__:

The alphametic does have two solutions but the second does not meet the given criteria. Identify why.

The alphametic does have two solutions:

**a. 857*187=160259**

**b. 807*287=231609 **

Only the **second** meets both criteria :

1.Both multiplicand 807 (3*269 ) and multiplier 287 (7*41) are semi-primes.

2. Since there is a difference of 1 between the number of hundreds and the number of units and there is 0 tens in 807 all partial products will consist of concatenation of two 2-digit numbers differing by 1 times the according multiplier's digit: 16-14=2; 64-56=8 and 56-49=7.

No need to check the 1st (a) triplet; it will not work.

So **807*287=231609** is the true solution, although labeled **2nd**

by the solver and **1st** by the author.