My Code

Primes

• Primes by trial division in C
• Primes by sieve in C
• Primes by sieve in Commodore 64 Assembler
• Primes by sieve in Python
• Primes by sieve using wheel factorization in C
• Mersenne primes using the Lucas-Lehmer method in C
• Fermat’s Little Theorem in C
• Density of primes in Python
• Twin primes of arbitrary length in Python
• Palindromic primes of arbitrary length in Python
• Explore anti-sameness bias in primes in Python

Ordinary Differential Equations

• Euler Method in Python
• Heun’s Method in Python
• Midpoint Method for ODE in Python

Newton-Cotes formulae for area under a curve in C

Each method integrates the curve f(x) = 5x^3 – 12x^2 + 7x – 3, and the integration is carried out from x = 2 to x = 6.  The analytic answer is area = 868.00.  The eight methods represented here are the eight Newton-Cotes formulae – four open and four closed.

• The trapezoid rule is the first degree closed Newton-Cotes formula.
• Simpson’s rule is the second degree closed Newton-Cotes formula.
• Simpson’s 3/8 rule is the third degree closed Newton-Cotes formula.
• Boole’s rule is the fourth degree closed Newton-Cotes formula.
• The rectangle rule is the second degree open Newton-Cotes formula.
• The trapezoid method is the third degree open Newton-Cotes formula.
• Milne’s rule is the fourth degree open Newton-Cotes formula.
• The fifth degree open Newton-Cotes formula has no name

Various

• Date of Easter in C
• A* path finding in IPython