A software for numerical calculations with large numbers was been made at the Faculty of Computer Science within the International Slavic University “Gavrilo Romanovich Derzhavin”. The software for numerical calculations with large numbers which can have several billion digits, can be used for empirical verification of the accuracy of:
𝐹𝑛⋅𝐹𝑛 + 1 ⋅𝐹𝑛 + 2 ⋅𝐹𝑛 + 3 ≡ 6 (𝑚𝑜𝑑𝐹𝑛 + 4): 𝑛∈ℕ, = 1,2,3
where 𝐹𝑛, 𝐹𝑛 + 1, 𝐹𝑛 + 2, 𝐹𝑛 + 3 and 𝐹𝑛 + 4 are Fibonacci numbers. The verification will be performed on the first 100 million (100,000,000) Fibonacci numbers and the software is expected to finish by processing the data in 1 week. One hundred million (100,000,000) have about twenty million (20,000,000) digits.