After some 24 years of teaching courses in statics, dynamics, strength of materials and thermodynamics I decided to retire on a high note (Excellence in teaching award from the College of Engineering at PSU in 2012) and co-authoring a paper in prime number theory (accepted but not published yet) in July of 2013.
Below you find links to material which are partially related to my past work
and partially to my present hobbies. You may contact me on any of the subjects listed below. Comments, questions and suggestions are most welcome, feel free to use either the "Send a Note to Zig" link or my email address.
Although there are some equations available which produce a large number of prime numbers these equations cannot be used to predict prime numbers in general. A classical example, dating back to Euler, is the equation :
f(n)=n2 + n + 41
which produces prime numbers for each n between 0 and 39 (inclusive) but mingles primes and composite numbers for larger n in seemingly random fashion.
Already a casual observation of the first, let's say hundred, prime numbers reveals that they seem to thin out. Still, it can be proven easily that there are infinitely many of them, see here for a proof due to Euclid (300 B.C.).
Related to that is the question as to how many prime numbers exists below a chosen value x. This is called the prime counting function, most often denoted by π(x) or pi(x). An excellent and short treatise of π(x) can be found at Chris K. Caldwell, How many primes are there, table, Values of pi(x) and analytical functions which approximate π(x) at Chris K. Caldwell, How many primes are there,approximations.
Having access to some computational resouces I participated in a research project on prime numbers which resulted in an article EMPIRICAL VERIFICATION OF THE EVEN GOLDBACH CONJECTURE AND COMPUTATION OF PRIME GAPS UP TO 4*1018 by Tomás Oliveira e Silva, Siegfried Herzog and Silvio Pard published in Math. Comp. 83 (2014), 2033-2060
Click here for more on prime numbers and gaps between adjacent prime numbers
A linear equation system solver (up to 20 unknowns)
Stuff on Stirling Engine