Calculator

What it's for

Do sums that ordinary calculators can’t: exact arithmetic on whole numbers of any size, with the modular maths, prime tests and factoring that RSA and capture-the-flag puzzles need. Switch to decimals for everyday sums with trigonometry and logarithms.

For example, when a puzzle gives you n, e and a ciphertext, factor n and work out the private key here.

How to use it

Type one expression per line; each line’s result appears beside it as you type. Set variables (p = 61) and use them on later lines; ans is the previous result. The functions are listed under the boxes. Numbers chooses exact whole numbers or decimals, and is remembered. Copy a link to this input keeps the lines.

Example

Choose Try an example, which works through the textbook RSA key with p = 61 and q = 53. The last line encrypts 65 and decrypts it again, and its result is 65.

Good to know

Whole-number division drops the remainder. Factoring gives up after three seconds and shows what’s left unfactored, so numbers with two large prime factors (real RSA keys) won’t factor. Prime tests are certain below about 3 × 10^24 and overwhelmingly likely above. Decimals have about 15 significant digits.