PRIMORIAL CONJECTURE

[Davide Rotondo]

After having found a conjecture similar to Buss's, which instead of considering the smallest number greater than f(n) + 1 considers the smallest number different from 1 that, when concatenated to f(n), gives a prime number, I propose today a variant of Fortune's primorial conjecture that uses concatenation. The first 100 values ​​are as follows.

[3, 7, 7, 11, 17, 17, 29, 29, 61, 37, 43, 41, 59, 61, 269, 79, 61, 89, 73, 101, 83, 109, 197, 107, 211, 173, 109, 379, 151, 127, 149, 211, 157, 181, 277, 179, 193, 179, 257, 211, 337, 277, 449, 307, 269, 251, 461, 487, 307, 311, 653, 281, 491, 617, 331, 409, 463, 389, 461, 283, 367, 307, 659, 491, 727, 743, 521, 499, 421, 521, 491, 409, 1151, 1097, 773, 593, 613, 859, 409, 431, 1019, 661, 827, 1549, 557, 683, 853, 1049, 643, 613, 601, 859, 733, 523, 719, 619, 761, 983, 557, 557]

Are these values always prime?

Davide

[Pontus von Brömssen]

What is f(n) here? It can't be the product of the previous terms (as in A067836), because then the third term wouldn't be 7: 3*7=21, but 217 = 7*31 is not prime.

Cheers, 

Pontus

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[Pontus von Brömssen]

Ah, I see: f(n) is the n-th primorial. Sorry.

Best regards,

Pontus