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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 0.665070048764852292... is the real root of f(x) = 1 + (twin_prime(n))x^n = 1 + 3x + 5x^2 + 5x^3 + 7x^4 + 11x^5 + 13x^6 + 17x^7 + 19x^8 + 29x^9 + 31x^10 + 41x^11 + 43x^12 + 59x^13 + 61x^14 + 71x^15 + 73x^16 + ... where for n>0 the coefficient of x^n is the nth twin prime. This power series with twin prime coefficients is similar to the power series with prime coefficients, as computed in Finch's article on Backhouse's constant. Jonathan Vos Post first described this pseudoBackhouse constant; T. D. Noe wrote the Mathematica code and computed it to 100 decimal places. T. D. Noe speculates that the constant is transcendental.
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