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By Stephen P. Richards

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PRIME RACES, EMIRPS, AND MORE 35 The setting up of these races in no way implies that we know anything about prime numbers in general. They are just formulated to cover all the odd numbers except for sets which are obviously composite and therefore contain no primes at all. Thus, for example, in the 'grouping by sixes' we are omitting the series of odd numbers which starts with 9 and adds sixes, since these are all obviously divisible by 3. In this same spirit it is possible to set up many more prime number races with even more 'horses', and it should not be difficult for you to invent some more for yourself.

On the other hand, as we have seen before, judging the trends of number sequences from their behavior through the first few powers of ten can be hazardous. Just how hazardous in the present context can be seen by considering that particular subgroup of emirps which have no repeating digit. Quite evidently, from the above examples, all the twodigit emirps fall into this category. It happens that 11 of the 13 threedigit emirps are also of the non-repeating-digit type, as are 42 of the four-digit emirps and 193 of the five-digit emirps.

Whether one series actually leads in the infinite limit (and by this we mean that there is some 'milepost' N beyond which one row stays ahead for ever), or whether one or more of the series eventually stop altogether with an absolute highest prime number of the required form, is just not known. In other words, for this and like cases the race may have a true winner or, on the other hand, one or even all of the number 'horses' may fail to complete the course. Unfortunately, the final outcome for any particular case is not likely to be determined by using a pocket calculator and a table of prime numbers.

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