# What is the average time for an honest network to find a block when its hash rate is p?

let p be the hash rate that belongs to honest network and T be the time a block is found. In the Bitcoin paper it's said "assuming the honest blocks took the average expected time per block...". In another paper it's said this average time is T/p.

Question: What is the average time for an honest network to find a block?

If it's T/p, why?

I think,

if p+q=1, where q is an attacker's hash rate and a block is found with the full hash rate: H, in T time. Then for an honest network, it would take, pT (not T/p).

Am I missing something?

I do not agree with the assumptions.

In the Bitcoin network, the average block time is also a function of the difficulty, approximately:

``````(P*d)/p = 10 minutes
``````

Where P is the average number of hashes to obtain a new block in 10 minutes (if d=1 and p=1 at base - it wasn't - then P=600), d is the current network difficulty and, p is the current network hash rate per second.

Presuming the honest network and the attacker both perform honest mining, the expected time till the honest network finds a block is T/p.

T is the expected time until any participant in the network finds a new block, p is the hash power of the honest network.

pT makes absolutely no sense since this would mean that a low hash rate will make you find blocks fast. In fact a participant with a mining power of 0 would be able to find a new block in 0*T = 0 time.