Yes. It is of course possible. You are allowed to modify the whole mining software if the resulting block is a valid bitcoin-block. But you donR17;t gain a 2x hash rate. It doesnR17;t make any difference wheather you try all numbers between 0 and 29 or you try all even numbers between 0 and 59 because they are still only 30 numbers.
What if you search downwards for a nonce?
As I said: You could do that. But it doesn’t make any difference in average. The normal case: The difficulty is very high. So you need to try all the nonce-numbers (0-4.294.967.296). If no one else mined the block, you can change the timestamp or modifiy the coinbase-text and try all the nonces again and again because the hashes will be completly different then.
Skipping (even, odd, every third, etc).
There is no advantage. It’s actually a little disadvantage because you need to calculate
nonce++ 2 times instead of 1 time or you need to do the if statement
if(nonce%30==0) or whatever instead of doing nothing. So you would waste energie, time and mining power instead of hashing a block.
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