Does anybody know how to estimate/calculate the total possible DPs within the range? Moreover, it is also possible that for some DP value there will not be any DPs.
For example, the minimum X-coordinate value I know is for private key 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0 and for 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1
Their X-coordinate has 90 leading zeros, so it is DP=90
Probably there are only 2 X-coordinates with 90 leading zeros, and no more.
There are about 2^256 points, then 2^255 different X-coordinates (k*G and -k*G have the same x-ccordinate).
Probably there are:
2^255 / 2 X-coordinates with 1 zero leading bit
2^255 / 4 X-coordinates with 2 zeros leading bits
….
2^255 / 2^90 X-coordinates with 90 zeros leading bits
…
If you sum 2^254 + 2^253 + ….+ 2^165 + …. = 2^254 (1/2 + 1/4 + 1/8 + ...) = 2^254 X-coordinates with at least 1 zero leading bit.
With DP very very large (like DP=250) you can manually determine how many x-coordinates there are (if there are) such that Y^2 = X^3 + 7 mod p