The Amazing Story of the Ruth-Aaron Numbers
In all humility I hesitated to add this item to the collection.
The mathematics is quite straightforward -- anyone with a passing knowledge
of the transcendentals such as pi will immediately grasp.
But first you have to get around the issue that in the United States a strange game called baseball
is played in which Babe Ruth and Hank Aaron have a status akin to that of Don
Bradman in a real ball sport.
Even mathematicians in the US have a passing knowledge of this game. Now Babe Ruth's career regular-season home run total
was 714, a record which Aaron eclipsed on April 8, 1974, when he hit his 715th career home run. So struggle on...
Thus 714 and 715 are the Ruth-Aaron Numbers. Got it? Read on!
The mathematician, and baseball follower, Carl Pomerance, named the numbers 714 and 715
the Ruth-Aaron Numbers, after a student discovered that 714 and 715 had (different) prime factors with the
But there was far more to be discovered about the Ruth-Aaron Numbers:
made the amazing discovery that the sum of the Ruth-Aaron Numbers,
714 and 715, is a backwards-forwards-sideways prime:
In detail: 714 + 715 = 1429.
This is a prime number -- its only factors are itself and(arguably) one.
The claim was that if you scrambled the digits in 1429
in accord to the backwards and sideways concepts,
-- you would still have a prime number. Thus:
- Forwards 1429 is prime
- Backwards 9241 is prime
- Sideways 9421 is prime
- Sideways 4129 is prime
- Sideways 4219 is prime
- sideways 1492 Eh? Eh?
So 1429, 9241, 1249, 9421, 4129, 4219 are all prime numbers.
As to 1492? That couldn't be more prime
to an American who called the competition in which Ruth and Aaron
played the World Series
1492 was the year that Columbus 'discovered' America.
What's more, 714 x 715 = 2 x 3 x 5 x 7 x 11 x 13 x 17 -- the product of the first seven primes. This must be the clincher !!
So we too accept
that 1429 is a backwards-forwards-sideways prime,
on the basis of sufficient kutzpah.