Google Calculator cheat sheet

I just found an awesome site describing some of the features in Google while looking for info on Google Calculator:  Google Guide

My first find was the Quick Reference: Google Calculator (Cheat Sheet).

I like this tip from Google Guide solutions to Calculator problems:

Compute the probability of your winning the lottery if you buy 1,000 tickets each bearing five distinct independently randomly chosen integers between 1 and 99.

The following answer was contributed by Nelson Blachman (Nancy's father).

You might try [ 1 - (1 - 1/(99 choose 5))^1000 ], but this is well approximated by [ 1000/(99 choose 5) ], which is roughly 0.00001 . If each ticket costs $1, the prize had better be at least $100 million to be fair to you — and higher if you might have to share the prize with other winners.

While I was on that train of thought, I found the Lottery Mathematics entry on Wikipedia.

Also...  I've always wanted to figure out the probability calculation for various poker hands.
 

One more interesting link:  Soople.com's Visual Interface to Google's calculator

Optimized prime number generator

Same specs as previous system, 8 hours to find all primes to ULONG_MAX.

#include <stdio.h>
#include <malloc.h>
#include <limits.h>
#include <math.h>

struct linked_list
{
    unsigned long number;
    struct linked_list *next;
};

int main(int argc, char **argv)
{
    unsigned long divisor, max_divisor, prime_test;
    unsigned long max_prime_to_store;
    struct linked_list *first=NULL, *current=NULL, *last=NULL;

    first=(struct linked_list *)malloc(sizeof(struct linked_list));
    first->number = 2L;
    first->next = NULL;
    last = first;
    printf("%lu\n", 2L);

    max_prime_to_store = 1L + sqrt(ULONG_MAX);

    for(prime_test = 3L; prime_test < ULONG_MAX; prime_test+=2L)
    {
        max_divisor=1L+sqrt(prime_test);
        for(current = first; current && current->number <= max_divisor; current = current->next)
        {
            if(prime_test % current->number == 0)
            {
                break;
            }
        }
        if(!current || current->number > max_divisor)
        {
            if(prime_test <= max_prime_to_store)
            {
                last->next = (struct linked_list *)malloc(sizeof(struct linked_list));
                last = last->next;
                last->next = NULL;
                last->number = prime_test;
            }
            printf("%lu\n", prime_test);
        }
    }
    return 0;
}

I miss C programming. Program to find prime numbers

Uses unsigned long long, goes up to ULONG_LONG_MAX.

Intel Core Duo 2 processor, running Cygwin on Windows XP, and compiled using gcc 3.4.4. Stops at first million results due to time. Can reasonably get to 10 million, if you're willing to wait.

#include <stdio.h>
#include <math.h>
#include <limits.h>

int main(int argc, char **argv)
{
    unsigned long long divisor, max_divisor, prime_test;
    int break_time = 0;

    printf("%llu\n", 2LL);
    for(prime_test = 3LL; prime_test < ULONG_LONG_MAX; prime_test+=2LL)
    {
        max_divisor=1LL+sqrt(prime_test);
        for(divisor=3LL;divisor <= max_divisor; divisor+=2LL)
        {
            if(prime_test % divisor == 0)
            {
                break;
            }
        }
        if(divisor >= max_divisor)
        {
            printf("%llu\n", prime_test);
        }
        else
        {
            continue;
        }
        break_time++;
        if(break_time == 999999)
        {
            break;
        }
    }
    return 0;
}