Here is the definition of private key in from bitcoinwiki:
"A private key in the context of Bitcoin is a secret number that allows bitcoins to be spent. Every Bitcoin wallet contains one or more private keys, which are saved in the wallet file. The private keys are mathematically related to all Bitcoin addresses generated for the wallet.
Because the private key is the "ticket" that allows someone to spend bitcoins, it is important that these are kept secure. Private keys can be kept on computer files, but in some cases are also short enough that they can be printed on paper.
Some wallets allow private keys to be imported without generating any transactions while other wallets or services require that the private key be swept. When a private key is swept, a transaction is broadcast that sends the balance controlled by the private key to a new address in the wallet. Just as with any other transaction, there is risk of swept transactions to be double-spending."
Do some reading. The answer is out there, it's public. Do a search for "RSA" the company which brought public/private key pair encryption to the market place.
There are 2 things to learn. asymmetric encryption/decryption and digital signatures with use this encryption.
One more time, a private key is created by multiplying two prime numbers together, the product of the multiplication becomes the public key.
7 prime number 1
11 prime number 2
7 * 11 = 77
77 is the public key
7 and 11 make up the private key.
77, the public key is used in math function to encrypt messages
7 and 11 remain private and only used by the person who wished to decrypt the messages.
I won't go into the math, it' not important and people can look it up if they want proof.
Next we can use this process of encryption and decryption to create digital signatures used by the bitcoin system to verify the true identity of a person who claims to have ownership of a receiving transaction. When you contact amazon.com to buy something, how do you really know it was amazon that sent you the web page before you give up your credit card number. Your computer uses encryption to verify the digital signature sent by amazon. I won't go into the details. Want proof, google "how do digital signatures work".
If we use prime numbers with thousands of digits to generate public keys all the computing power on earth could not factor out the individual primes used to make that public key in billions of years. The NSA the largest code breaking entity in history is powerless against this encryption.
