MC Frontalot
More by cryptogeek:
More Life Among the Nerd Folk:

Frontalot Primes: A New Class Of Prime Numbers

Introduction
In this document, we will introduce a new class of prime numbers having specific, novel, but mathematically uninteresting properties. We go on to state a few facts about such primes, provide one example of such a prime, and give a few conjectures about this new class of primes.

Definition
Let P be an odd positive prime number. P is a "Frontalot" prime if log10(P) >= 1000 (i.e., P is a titanic prime), and the big-endian binary expansion of P includes the ASCII representation of the letters "MC Frontalot" (including the space). In hexadecimal, the representation of P would have to include the following sequence, beginning on an even hexadecimal digit: 0x4d432046726f6e74616c6f74.

A Brief Overview
From a mathematical standpoint, Frontalot primes have no special properties that make them useful or interesting. Frontalot primes do not admit any special relation to twin primes, Sophie Germain primes, Mersenne primes, Fermat primes, or other primes of special form. There is no known special relation between Frontalot primes and the Goldbach conjecture, the Riemann hypothesis, or the twin prime conjecture. They are, in a sense, only interesting for the sake of having a bad-ass rapper's name embedded within them.

Frontalot primes, however, may prove fascinatingly interesting to some fans of a musical genre called "Nerdcore hip-hop", and the future study of such primes will likely fall to these nerds.

Note that the hexadecimal digits which qualify a number as a Frontalot prime form an even number. It is therefore impossible to find a Frontalot prime whose second condition is satisfied entirely within the lowest 96 bits of its binary representation.

Conjectures

Frontalot Prime Conjecture: There are infinitely many Frontalot primes.
Frontalot Factorial Conjecture: There exists a Frontalot Prime of the form (n! +1) or (n! - 1)
Frontalot Twin Conjecture: There exist infinitely many pairs of Frontalot primes, P1 and P2, such that P2 = P1 + 2.

Proofs are left as exercises to the interested reader.

Example Frontalot Prime
The first known Frontalot prime, located using a custom number theory library and proved prime using the well-regarded Primo program is (represented here in hexadecimal):
ff4d432046726f6e74616c6f7400000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004ab

Conclusion
We have introduced a new class of prime numbers, called Frontalot primes, and discussed their sole source of interestingness. We have developed a set of conjectures regarding this new class of primes, closely related to more general conjectures about prime numbers. Finally, we have proved the existence of such primes by providing an example of a prime of this class.

NERDLIFE by cryptogeek :: 7.21.08 :: VSP #29