Phil Carmody sends the following nice alphametic puzzle (each letter stands for a different digit):

I have a PRIME NUMBER PROBLEM - they're all prime! NINE is prime, MILLION is prime too. Even ONE is prime.

Questions: Just solve it.

Well, this puzzle became very popular. Contributions came from A. Rupinski, Faride Firoozbakht, Robin García, Ken Wilke, Ray Opao, J.C. Rosa, Anurag Sahay, Joseph L Pe and J. Wiessenbauer. All of the found the following solution:

{239,3539,41579,307691,7588523,4126897,{6,9,5,8,7,3,2,4,1,0}} for ONE, NINE, PRIME, NUMBER, MILLION, PROBLEM, & b,e,i,l,m,n,o,p,r,u.

Only Faride and Rosa found the other three solutions:

{031,3631,87691,359417,9622603,8704219,{4,1,6,2,9,3,0,8,7,5}}
{097,9497,83417,961273,1455409,8302571,{2,7,4,5,1,9,0,8,3,6}}
{097,9697,81637,923471,3655609,8104573,{4,7,6,5,3,9,0,8,1,2}}

Here is the Faride's computer-approach:

I used the following facts.

1) E,M,N & R are distinct members of {1,3,7,9}.
2) B,I,L,O,P & U are distinct members of {0,2,4,5,6,8}.
3) ONE,NINE,PRIME,NUMBER,PROBLEM & MILLION are primes.

It takes only 130.016 Seconds.
For finding the solutions I used the following program (in Mathematica).

Timing[ca[a_]:=(v1={};t=Length[a];
Do[v1=Join[v1,IntegerDigits[a[[k]]]],{k,t}];
FromDigits[v1]);
v=Permutations[{1,3,7,9}];
Do[{e,m,n,r}=v[[j]];s=Length[v];
Do[If[Union[{b,i,l,o,p,u}]=={0,2,4,5,6,8}&&
PrimeQ[ca[{o,n,e}]]&&PrimeQ[cca[{n,i,n,e}]]&&
PrimeQ[ca[{p,r,i,m,e}]]&&
PrimeQ[ca[{n,u,m,b,e,r}]]&&
PrimeQ[ca[{m,i,l,l,i,o,n}]]&&
PrimeQ[ca[{p,r,o,b,l,e,m}]],
Print[{ca[{o,n,e}],ca[{n,i,n,e}],ca[{p,r,i,m,e}],
ca[{n,u,m,b,e,r}],ca[{m,i,l,l,i,o,n}],
ca[{p,r,o,b,l,e,m}],{b,e,i,l,m,n,o,p,r,u}}]],
{l,0,8},{p,0,8},{u,0,8},{o,0,8},{b,0,8},{i,0,8}],{j,s}]]

***