Having written about prime chains of the Cunningham variety in my previous post, I find that today's prime number (24499) also forms the start of a prime chain. Specifically, the number is part of OEIS A023315: numbers \(n\) such that \(n\) remains prime through four iterations of function \(f(x)=5x+6\). The numbers listed are:
79, 401, 1259, 2477, 3019, 4409, 10303, 15679, 20509, 24499, 34127, 43987, 44389, 53101, 66359, 71287, 74857, 81097, 85903, 90803, 93053, 102811, 103231, 104999, 112601, 125453, 132533, 144731, 156347, 157793, 160817, 161839, 163981, 170641
Confirming this, we have:
- 24499 x 5+6 = 122501 (prime)
- 122501 x 5+6 = 612511 (prime)
- 612511 x 5+6 = 3062561 (prime)
- 3062561 x 5+6 = 15312811 (prime)
- 15312811 x 5+6 = 76564061 (factors to 7×10937723)
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