| The mathematician and astronomer Thabit ibn Qurra studied these numbers in search of a formula for amicable pairs. He found that when two consecutive Thabit numbers are also prime numbers (corresponding to indices $n$ and $n - 1$) and $9 \cdot 2^{2n - 1} - 1$ is a prime number, too, then these numbers multiplied by $2^n$ will reveal an amicable pair. The only $n$ known to fit these criteria are 2, 4 and 7. The largest Thabit number known to be prime corresponds to index 2312734, its immediate lower neighbor is composite. |
The mathematician and astronomer Thabit ibn Qurra studied these numbers in search of a formula for amicable pairs. He found that when two consecutive Thabit numbers are also prime numbers (corresponding to indices $n$ and $n - 1$) and $9 \cdot 2^{2n - 1} - 1$ is a prime number, too, then these numbers multiplied by $2^n$ will reveal an amicable pair. The only $n$ known to fit these criteria are 2, 4 and 7. The largest Thabit number known to be prime corresponds to index 2312734, its immediate lower neighbor is composite. |
