User:PrimeFan

I am a fan of prime numbers. I have been researching "prime deserts", such as those enclosed by factorial primes. I also like to look for twin primes immediately preceding or following such deserts.

I have started articles on factorial prime, primorial prime, permutable prime, primorial, palindromic prime, negative one, one half, harmonic divisor number, strobogrammatic prime, Kaprekar number, Keith number, some figurate numbers (such as pentagonal numbers, tetrahedral numbers, centered square numbers), cuban prime, unitary perfect number, Smith number, heteromecic number, prime quadruplet, Motzkin number, self number, untouchable number, noncototient, Friedman number, Wedderburn-Etherington number, highly totient number, safe prime, amenable number, highly cototient number, Thabit number, self-descriptive number, Giuga number, Markov number (with a redirect from Markoff number), pandigital number, exponential factorial, Stern prime, Higgs prime, Levy's conjecture. I helped expand the stub on Harshad number. I have also edited pages on various numbers and mathematical concepts. It was, as a matter of fact, the articles on the individual integers from one to one hundred that at first drew me to Wikipedia.

Pages I Plan To Create (Or Work On If Created By Someone Else)

• Alternating factorial
• Antiprime According to Mathworld this is just another term for highly composite number, but the OEIS has a different idea.
• Cluster prime
• Cunningham number These are mentioned on Paul Leyland's personal home page, but as of this writing Wikipedia doesn't seem to have an article on them
• Dihedral prime
• Giuseppe Giuga Mathematician who studied Giuga numbers
• Lagrange number possibly with redirect from LaGrange number
• Rhombic dodecahedral number
• Unitary divisor (perhaps as an addition to the article on divisor)
• Unprimeable number? (Numbers such as 200, which in a given base can not be turned to a prime number with just one digit changed. I don't know if there's an official name for this concept bestowed by a professional mathematician).
• Veryprime

Handy Links

• Sloane's OEIS Integer Sequence Look-Up
• Matthew Conroy's Java Dictionary of Numbers

Some Kinds Of Primes I've Been Thinking About

One of these days I need to update this section. RecentlyUser:PrimeHunter has given me some insights on 10^n + 1 primes and Euler's lucky numbers and I will be reflecting on those.

I'm fascinated by repunit primes in various bases while simultaneously feeling a bit guilty about devoting too much time to kinds of primes that are base-dependent, such as Smarandache-Wellin primes.

Related somewhat to base 10 repunits are primes of the form 10ⁿ + 1, which can be defined in a base-dependent way as well as in an algebraic form. So far the only primes I know of this form are 2 (which is a consequence of the algebraic definition, not the base-dependend one), 11 and 101. I've gone up to 10⁵⁰ + 1 and found no other primes, but at least I've noticed some patterns. If n is odd then 10ⁿ + 1 will be divisible by 11. If n is divisible by 2 but not by 4, then 10ⁿ + 1 will be divisible by 101. 73 and 137 are two other numbers I've seen a lot in the factorizations, but no pattern is apparent to me right now.

Also, I've been looking for primes greater than 41 such that n² + n + p equals a prime when n is between 0 and (p - 1). The primes less than 41 that meet this criterion are 3, 5, 7, 11 and 17. It should've been obvious to me that the number I'm looking for must be the lower of a twin prime, but at least knowing that helps me in my future searches. It's entirely possible that there are no such primes beyond 41, and that that can be proven by using congruences. But if it needs calculus to be proven, then I have an excuse for not knowing that proof.

With the enduring popularity of Mersenne primes and Fermat primes, I've wondered why people aren't researching other primes of the form pⁿ - (p - 1) or pⁿ + (p - 1). But they are. For example, I calculated the first six n for which 3ⁿ + 2 is prime, put that into Sloane's OEIS look-up, and sure enough, the second result was sequence A051783, "Numbers n such that 3^n + 2 is prime."

Lastly, I've been thinking about prime numbers that are also figurate numbers other than F₂, because every positive integer is, if nothing else, an F₂ figurate number. For example, 7 is a heptagonal number, 13 is a 13-gonal number and 127 is a 127-gonal number. What might not be so obvious is that 13 is a star number and 127 is a centered hexagonal number. As far as I can tell, centered polygonal numbers are the only kind of F_x<>2 number prime numbers can be.

McDononald's Monopoly Game Piece Numbers

I've noticed that McDonald's Monopoly game pieces have four digit numbers on them, and that the first two digits correspond to the iteration of the game and the second two to the location on the Monopoly board. (Thus, you can't win the million dollars with a Boardwalk from the first iteration of the game and a Park Place from the latest iteration of the game -- not that I have ever gotten a Boardwalk).

1. Mediterranean Avenue
2. Baltic Avenue
3. Oriental Avenue
4. Vermont Avenue
5. Connecticut Avenue
6. St. Charles Place
7. States Avenue
8. Virginia Avenue
9. St. James Place
10. Tennessee Avenue
11. New York Avenue
12. Kentucky Avenue
13. Indiana Avenue
14. Illinois Avenue
15. Atlantic Avenue
16. Ventnor Avenur
17. Marvin Gardens
18. Pacific Avenue
19. North Carolina Avenue
20. Pennsylvania Avenue
21. Park Place
22. Boardwalk
23. Reading Railroad
24. Pennsylvania Railroad
25. B. & O. Railroad
26. Short Line

My Life Story (If You Care To Hear It)

I served in the United States Navy for four years. After that, I worked in various factories for thirty-five years, getting cut short of retirement by a weird accident, from which I thankfully recovered quickly (relatively). During my time in the hospital, bored by television, I turned to books and gradually became interested in mathematical topics to an extent I would not have foreseen as a youngster. I stumbled on Wikipedia while researching prime numbers on the Web, and that brings us up to present times.

Awards and Such

For your splendid contributions to Wikipedia's sections on mathematics and numbers, I'm sending this Barnstar your way. Mr. Billion 00:48, 8 Jan 2005 (UTC)