By Stephen P. Richards
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Etc. It is obvious that any 'single-repeating-digit' number, like 7,777,777 for example, cannot possibly be prime because it is exactly divisible by the digit itself (in this case 7). This is true unless, of course, the digit in question happens to be a 1. The number 1, 111,111, for example, is not obviously composite. Are there any prime numbers of this sort? This question is easily answered because the very smallest example of such anum ber, namely 11, is itself a prime. But are there any more?
It has been called the largest number which has ever served a useful purpose in mathematics, and mathematical numbers always exceed by far those used in the other sciences. For example, the total number of atoms in the entire universe is 'only' about 1075 • This last number, written out in full, is a 1 followed by 75 zeroes. The monstrous number above, on the other hand, has no less than 10 1034 zeroes. This means that, even if we used as many zeroes as there are atoms in the universe, we still could not come close to writing it out in full.
Is there a good example of one ending with a 7? Indeed there is, the longest yet discovered in fact. It begins, as required, with 1234 .... and cycles seven times before finishing with 1234567. THE BAFFLING LAW OF BENFORD 43 6. THE BAFFLING LAW OF BENFORD The origin of the unusual phenomenon to be discussed in this chapter is said to go back ~to an observation, commonplace before the era of the pocket calculator, that log tables in public libraries appeared to be dirtier at the beginning than at the end.
A Number for Your Thoughts by Stephen P. Richards