Of the 1052 four-digit primes, eliminate those with duplicated digits and particularly which do not contain three digits of 1, 3, 7 or 9, to yield 125 prime numbers having four unique digits.  Of these, sixteen pairs have the same first two digits with the last two digits reversible (as in POTS and POST).  Of these, further eliminate those starting with an even number or 5 (since POTS does reverse to STOP), to yield the following nine candidate pairs for POTS and POST:

1039/1093

1279/1297

1439/1493

1579/1597

3217/3271

3517/3571

3617/3671

9137/9173

9817/9871

Of these, only the seven underlined numbers, when completely reversed, yield the following prime candidates (in order) for STOP:

9721

9341

7951

1723

1753

3719

1789

Of these seven possibilities for STOP, move the first digit to last to yield TOPS:

7219

3419

9517

7231

7531

7193

7891

The only two possibilities for TOPS which are prime numbers are underlined, with T = 7 in both cases.  Assigning these two sets of possible digit values to TOPS, SPOT, POTS, STOP, POST and OPTS then yields:

7219

9127

1279

9721

1297

2179 = 30822 = KAZOO

or,

7193

3917

9173

3719

9137

1973 = 35112 = SWOON

Edited on March 9, 2010, 11:41 am

Posted by rod hines on 2010-03-08 15:14:35