**From New Scientist #2372, 7th December 2002** [link]

I have constructed a chain of ten 2-digit prime numbers. The ten primes that I have used are all different and except in the case of the first prime in the chain each prime’s first digit is the same as the previous prime’s second digit. In addition the fourth prime is the reverse of the first prime, and the tenth prime is the reverse of the seventh prime.

What (in this order) are the third, sixth and ninth primes in this chain?

[enigma1216]

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This Python 3 program constructs all possible length 10 chains, and then checks the additional conditions. It runs in 84ms.

Solution:The third prime in the chain is 73. The sixth prime in the chain is 19. The ninth prime in the chain is 17.The entire chain is: (13, 37, 73, 31, 11, 19, 97, 71, 17, 79).