**Busting Bitcoin Myths: Myth #002 – There aren’t enough Bitcoin Addresses**

Hass McCook | 9 April 2014

**The Myth**

*“Because bitcoin wallet addresses are randomly generated, it is likely that someone else will generate the same address as me, and take all of my money.”*

**The Facts**

In non-technical terms, a bitcoin address consists of a string of case-sensitive alpha-numeric characters, with 2^{160} addresses available (in technical terms, an address is a 160-bit hash of a 256-bit cryptographic key pair, hence 2^{160}). To put that number in words, it’s roughly 1.46 million-quadrillion-quintillion, or, 1.46 with 47 zeroes next to it. If that was too much of a mouthful, here’s a graphic version which compares number of possible bitcoin addresses with the number of drops of water in the ocean, and number of stars in the observable universe – in logarithmic scale. The number of grains of sand on earth was not large enough to feature meaningfully on this graph.

To flog the dead horse further, the below is a table showing how long it would take to get through all of the bitcoin addresses if everyone on Earth (assuming 10 billion people to allow for population growth) were generating several addresses per second.

Doing Some Statistics

If we have 10 billion people on Earth, with a million addresses each, what is the chance that two of them pick the same address out of a pool of 2^{160} addresses? The chance of a match is 1 / 2^{160} , and there are “10-million-billion multiplied by 10-million-billion-minus-one” opportunities for a matching pair, making the probability of a matched pair 10E+32 / 2^{160}, or,0.000000000001110%.

**Conclusion – Making Sense of the Numbers**

Although the chance of two people generating the same address is not zero, it is so infinitesimally small that it can be considered to be zero. So go forth and generate as many addresses as you like without fear – there are plenty to go around!

**References:**

https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses

http://hypertextbook.com/facts/2001/SyedQadri.shtml

http://www.nature.com/nature/journal/v468/n7326/full/nature09578.html

http://www.hawaii.edu/suremath/jsand.html

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