How to change the field of the elliptic curve to the new value N while keeping the default Secp256k1 parameters? I want to change the margin of the elliptic curve to the new N value, while doing so I want to keep the parameters Standard G-point Generator Secp256k1 that is, I want to replace: N = 115792089237316195423570985008687907852837564279074904382605163141518161494337
to the new value: N = 115792089237316195423570985008687907853269978629958289035461602417822422574827
leave the Secp256k1 parameters:
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424

P = 115792089237316195423570985008687907853269984665640564039457584007908834671663

For the calculation, I use a Python script:
but in the end I get the same result as in the standard Secp256k1 parameters
that is, with Private key 2, I get
Public Key:
04C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE51AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A
Public Key (compressed):
02C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5

the result is the same as in the field N = 115792089237316195423570985008687907852837564279074904382605163141518161494337
What exactly am I doing wrong because I have set a new field? N = 115792089237316195423570985008687907853269978629958289035461602417822422574827
What needs to be changed so that as a result the Public Key is different from the standard Secp256k1 parameters?
Code :
Pcurve = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 -1 # The proven prime
Acurve = 0; Bcurve = 7 # These two defines the elliptic curve. y^2 = x^3 + Acurve * x + Bcurve
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
GPoint = (Gx,Gy) # Generator Point

N = 115792089237316195423570985008687907853269978629958289035461602417822422574827
privKey = 2

def modinv(a,b=Pcurve): #Extended Euclidean Algorithm/'division' in elliptic curves
    lm, hm = 1,0
    low, high = a%b,b
    while low &gt; 1:
        ratio = high/low
        nm, new = hm-lm*ratio, high-low*ratio
        lm, low, hm, high = nm, new, lm, low
    return lm % b

def ECAdd(a,b): # Point addition, invented for EC.
    LambdaAdd = ((b[1] - a[1]) * modinv(b[0] - a[0],Pcurve)) % Pcurve
    x = (LambdaAdd * LambdaAdd - a[0] - b[0]) % Pcurve
    y = (LambdaAdd * (a[0] - x) - a[1]) % Pcurve
    return (x,y)

def ECDouble(a): # Point Doubling, also invented for EC.
    LamdaDouble = ((3 * a[0] * a[0] + Acurve) * modinv((2 * a[1]), Pcurve)) % Pcurve
    x = (LamdaDouble * LamdaDouble - 2 * a[0]) % Pcurve
    y = (LamdaDouble * (a[0] - x) - a[1]) % Pcurve
    return (x,y)

def ECMultiply(GenPoint,privKeyHex): #Double &amp; add. Not true multiplication
    if privKeyHex == 0 or privKeyHex &gt;= N: raise Exception(&quot;Invalid Private Key&quot;)
    privKeyBin = str(bin(privKeyHex))[2:]
    Q=GenPoint
    for i in range (1, len(privKeyBin)):
        Q=ECDouble(Q);
        if privKeyBin[i] == &quot;1&quot;:
            Q=ECAdd(Q,GenPoint);
    return (Q)

publicKey = ECMultiply(GPoint,privKey)
print &quot;Private Key:&quot;;
print privKey; print
print &quot;Public Key (uncompressed):&quot;;
print publicKey; print
print &quot;Public Key (compressed):&quot;;
if publicKey[1] % 2 == 1: # If the Y coordinate of the Public Key is odd.
    print &quot;03&quot;+str(hex(publicKey[0])[2:-1]).zfill(64)
else: # If the Y coordinate is even.
    print &quot;02&quot;+str(hex(publicKey[0])[2:-1]).zfill(64)
The elliptic curve is secp256k1: y2 = x3 + 7 (mod p)
where the field size is
p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F.
The curve order of secp256k1 is:
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
The public key P (point) is calculated by multiplying the private key d (scalar) by the generator point G (point) where
P = d (mod n).G
The n (N) you state is not the field size p, it is the curve order
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
This curve order n is such that nG = point at infinity. This is a property of the curve and cannot be changed.
Thanks to Pieter Wuille for the corrections.