1000-digit Fibonacci number

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n−1 + F_n−2, where F₁ = 1 and F₂ = 1.

Hence the first 12 terms will be:

F₁ = 1 F₂ = 1 F₃ = 2 F₄ = 3 F₅ = 5 F₆ = 8 F₇ = 13 F₈ = 21 F₉ = 34 F₁₀ = 55 F₁₁ = 89 F₁₂ = 144

The 12th term, F₁₂, is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?

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