Why you ask, has Sheldon always said: “73 Is The BEST Number”!

73 is the best number because it has some seemingly unusual properties. First note that not only is 73 a prime number, its index in the sequence of primes is the product of its digits, namely 21: it is the 21st prime. In addition, reversing the digits of 73, we obtain the prime 37, which is the 12th prime, and 12 is the reverse of 21. 

To prove our theorem that 73 is the only Sheldon prime we will make use of the mirror property in addition to the product property. For example, the reverses of the 4 primes above are all composite, so they are instantly ruled out as Sheldon primes. Though the bound 1045 may seem daunting, we see at least that the search for Sheldon primes is finite. Our basic strategy is to use numerically explicit versions of the prime number theorem, similar to, but finer than, (1) to give us some of the leading and trailing digits of candidate primes, and use these to, we hope, eliminate them. Further, our search is not over all primes to 1045 but over integers n with pn < 1045.
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