On 12/19/2018 9:06 AM, Bruno Marchal wrote:
Diophantine equation, which are provably equivalent with the two
combinator law above. That is far longer to prove, of course, and this
results comes from the 50 years of hard work by Putnam, Davis,
Robinson (Juila), and Matiyasevic. The polynomial below if from
Matiyasevic and Jones:
Nu = ((ZUY)^2 + U)^2 + Y
ELG^2 + Al = (B - XY)Q^2
Qu = B^(5^60)
La + Qu^4 = 1 + LaB^5
Th + 2Z = B^5
L = U + TTh
E = Y + MTh
N = Q^16
R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + +
LaB^5Q^4)Q^4](N^2 -N)
+ [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1)
P = 2W(S^2)(R^2)N^2
(P^2)K^2 - K^2 + 1 = Ta^2
4(c - KSN^2)^2 + Et = K^2
K = R + 1 + HP - H
A = (WN^2 + 1)RSN^2
C = 2R + 1 Ph
D = BW + CA -2C + 4AGa -5Ga
D^2 = (A^2 - 1)C^2 + 1
F^2 = (A^2 - 1)(I^2)C^4 + 1
(D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1
X and Nu are the only parameters. The rest are variables. That is a
system of polynomials, which is Turing universal. For some value of
Nu, it generates the prime numbers. For some other value of Nu, it
simulates any digital computational process.
You mean it has X={primes} as solutions for some value of Nu? So X is
also a variable.
Brent
Bruno
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