Interesting!! However, in this case, you're not skipping keys; you're transposing the range from 2000:6000 to 1000:3000, which results in the same number of keys.
you avoid keys if you use the pubkey corresponding to pk 2, you would omit the odd private keys.
Why and how do you change the G? If you change the generator all the results will be incorrect for secp256k1 curve, maybe you mean to use a stride of 2, in order to skip 1 key between each jump, or skip 2, well if you try that you will see that you are just skipping for example 33% of the range as well as reducing the probability of finding your target by 33%.
But there is a way to do the search for public key faster, first you need to subtract as many keys as you can to have a new and ideally small range key, then you could generate +1 billion offsets and -1 billion offsets to keep in a file for auto comparison, then you could use a stride in such a way that each stride never goes beyond 2 billion keys, that way you are certain each stride will definitely have a 100% chance of landing on one of the 2 billion saved public keys.
Now for someone with serious RAM and speed, they can generate +10 & -10 billion keys to check and use a bigger stride to search faster.😉
pk= 1
pub_x= 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
pub_y= 483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
pub_dec_x= 55066263022277343669578718895168534326250603453777594175500187360389116729240
pub_dec_y= 32670510020758816978083085130507043184471273380659243275938904335757337482424
These are the standard bitcoin parameters (secp256k1).
# Elliptic curve parameters (secp256k1)
P = 2**256 - 2**32 - 977
N = 115792089237316195423570985008687907852837564279074904382605163141518161494337
A = 0
B = 7
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
G = (Gx, Gy)
Gx & Gy correspond to pubkey from pk #1
if we change these by the pubkey(x,y) of pk #2
pk= 2
pub_x= c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5
pub_y= 1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a
pub_dec_x= 89565891926547004231252920425935692360644145829622209833684329913297188986597
pub_dec_y= 12158399299693830322967808612713398636155367887041628176798871954788371653930
P = 2**256 - 2**32 - 977
N = 115792089237316195423570985008687907852837564279074904382605163141518161494337
A = 0
B = 7
Gx = 89565891926547004231252920425935692360644145829622209833684329913297188986597
Gy = 12158399299693830322967808612713398636155367887041628176798871954788371653930
G = (Gx, Gy)
we will get
pk=1
pub= 02c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5
pk=2
pub= 02e493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13
pk=3
pub= 03fff97bd5755eeea420453a14355235d382f6472f8568a18b2f057a1460297556
2, 4, 6....
that's what I mean.
And as for the decrease in the range of the pubkey, I'm on to something, which since you didn't understand before, I prefer to reserve it for the future.