Quote from: BurtW on September 12, 2013, 03:57:17 PM

The integer p specifying the finite field F_p can be found here:

https://en.bitcoin.it/wiki/Secp256k1

which is really just copied from section 2.7.1 "Recommended Parameters secp256k1" on page 15 of this document:

http://www.secg.org/collateral/sec2_final.pdf

I will verify this and then fix the wiki if I am correct.

The number is found in the wiki here:
https://en.bitcoin.it/wiki/Private_key#Range_of_valid_private_keys

And is frequently stated throughout bitcointalk.org:

https://bitcointalk.org/index.php?topic=157820.msg1672366#msg1672366

Quote from: deepceleron on March 25, 2013, 10:58:37 AM

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Also, SHA256 can create a value invalid as an ECDSA private key, "Specifically, any 256-bit number between 0x1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141 is a valid private key."

https://bitcointalk.org/index.php?topic=211503.msg2222704#msg2222704

Quote from: dunand on May 21, 2013, 01:21:12 PM

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Quote from: https://en.bitcoin.it/wiki/Private_key

Nearly every 256-bit number is a valid private key. Specifically, any 256-bit number between 0x1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141 is a valid private key.

The range of valid private keys is governed by the secp256k1 ECDSA standard used by Bitcoin.

https://bitcointalk.org/index.php?topic=165347.msg1727476#msg1727476

Quote from: Dabs on April 03, 2013, 04:01:22 AM

Quote from: dscotese

Does every number with the right number of bits represent a valid private key? That seems doubtful to me.

I think there is a range. I found it on the wiki: Specifically, any 256-bit number between 0x1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141 is a valid private key.
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https://bitcointalk.org/index.php?topic=162666.msg1715086#msg1715086

Quote from: DannyHamilton on April 01, 2013, 02:56:21 PM

Quote from: falcoiii on March 31, 2013, 06:10:03 PM

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What is the maximum number of private addresses?

2^96 -- https://bitcointalk.org/index.php?topic=24268.0

and "almsot 2^256" -- https://en.bitcoin.it/wiki/Private_key
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I assume you mean private keys (not private addresses, there is no such thing). In that case:

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

Quote

Nearly every 256-bit number is a valid private key. Specifically, any 256-bit number between 0x1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141 is a valid private key.

The range of valid private keys is governed by the secp256k1 ECDSA standard used by Bitcoin.

https://bitcointalk.org/index.php?topic=164687.msg1720529#msg1720529

Quote from: Dabs on April 02, 2013, 07:25:41 AM

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Nearly every 256-bit number is a valid private key. Specifically, any 256-bit number between 0x1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141 is a valid private key.
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https://bitcointalk.org/index.php?topic=156845.msg1662810#msg1662810

Quote from: kokjo on March 23, 2013, 11:50:04 AM

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its because the prime number chosen for secp256k1 is just a little less then 2^256

0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141 is that prime number in hexadecimal.

https://bitcointalk.org/index.php?topic=286534.msg3081656#msg3081656

Quote from: Sothh on September 04, 2013, 05:47:46 PM

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If you do it this way, the max address you can use is FFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141

https://bitcointalk.org/index.php?topic=271486.msg2970259#msg2970259

Quote from: gmaxwell on August 20, 2013, 09:37:51 AM

Quote from: jackjack on August 20, 2013, 09:16:41 AM

By the way its not really an upper limit: n+1 is a pretty valid private key, it's just that it's equal to 1 (as n+1 mod n == 1 mod n)

If you generate that way you will end up with keys which are not equiprobable. The difference from uniform is very small, but its a certificational weakness you should avoid.