..........
Seriously..
1.Chose whatever range, like I said, for the moment I have tested until puzzle 130, generate Yourself a hex private key in between chosen range and get the address.
2 Convert the hash160 of that address to decimal string.
3.Convert the hexadecimal private key to decimal as well,
4 Now using a big integer calculator for example
http://www.javascripter.net/math/calculators/100digitbigintcalculator.htm ( I am also using it ) divide the decimal string of hash160 by decimal version of private key
5.The resulting string now You have to multiply times decimal private key.
6 That multiplication will result with a long string of course but quite similar with the first digits like so basically that string will be required by me.
Tested your theory... There's something to it, but very insignificantly. And with additional tests, it tends to ordinary chaos...

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PK (hex): 000000000000000000000000000000020000000000000000000000E8D4A50FFF
ADR: 13qD8Bs6Kx8gQmuH7hWVfWTHPBXRGJ94aW
hash160 (hex): 1f0e5698f426c93197f6fe4561913d2dca7b0f56
hash160 (dec): 177298468032361376284751942974563620350777298774
PK (dec): 680564733841876926926749215863536422911
Quotient from division: 260516684
Result of quotient * private_key_dec: 177298467707828357339067016616368705409995347124
hash160: 177298468032361376284751942974563620350777298774
Prod: 177298467707828357339067016616368705409995347124