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+# Pumpkin
+
+A cryptographically-secure pseudo-random number generator for generating large 
+prime.
+
+## What's up with the name?
+
+Since I began writing this library around Halloween of 2015, I wanted to choose
+a name that was vaguely related to the holiday. Because "pumpkin" and "prime"
+both begin with the letter 'p', I decided to use that. And that's all there
+really is to it!
+
+## Purpose
+
+`pumpkin` is a cryptographically-secure pseudo-random number generator, which is
+useful for generating large prime numbers for cryptography. In fact, `pumpkin`
+can ONLY be used to generate prime numbers. On the back-end, `pumpkin` uses the
+wonderful [ramp](https://crates.io/crates/ramp) library for storing the large
+numbers. `pumpkin` generates numbers very quickly, so you can be sure that your
+program will be performative. In our testing, primes were generated anywhere
+between 1s and 5s on average, though of course your mileage may vary.
+
+## Example
+
+```
+extern crate pumpkin;
+
+use pumpkin::Prime;
+
+fn main() {
+    let p = Prime::new(2048); // Generate a new 2048-bit prime number
+    let q = Prime::new(2048);
+    let e = p * q;
+
+    println("{}", e);
+
+    /*
+     * 75222035638256552797269351238215022250546763213674706... Some massive
+     * 4096-bit number.
+     */
+}
+```
+
+## Explanation
+`Prime`s are generated much the same way that large primes are generated by
+`GnuPG`:
+  1) Create a large candidate number of size based on the input given to the
+  `Prime::new()` method. All `Prime`s must be at least 2-bits long (thoug it
+  wouldn't make much sense to be that small.
+
+  2) Divide the candidate number by the first 1,000 prime numbers.
+
+  3) Test the candidate number with [Fermat's Little
+Theorem](https://www.wikiwand.com/en/Fermat's_little_theorem).
+
+  4) Finally, run five iterations of the [Miller-Rabin Primality
+Test](https://www.wikiwand.com/en/Miller%E2%80%93Rabin_primality_test).
+
+`Prime`s are seeded by `rand::OsRng`, which receives its entropy via the
+operating system's own entropy source (such as `/dev/urandom'). Thus, because we
+can be confident that the generated candidate number is truly random (or as
+close to truly random as the user can hope), we don't need to do more than five
+iterations of the Miller-Rabin test to ensure primality.
+
+`Prime`s are simple "newtype" structs; that is, it is a tuple-like struct
+surrounding an `Int` type. `Prime`s have all of the basic algebraic and logical
+operators implemented, thus allowing you to do any operation that you would
+require.
+
+## Contributing
+
+`pumpkin` is dual-licenced under the MIT and Unlicense. Should you wish to
+contribute updates to the project, please consider signing the included `WAVER`
+file with your cryptographic digital signature (as allowed by your country's
+laws). Doing so will release your changes back into the public domain to be used
+freely by all. I did so with this project, and it would mean a lot if you did
+too!