Are there an infinite number of prime quadruples of the form , , , ?
In base , any prime number greater than 5 must end with the digits 1, , , or . For some , , , , are all prime: for example, when , we have that , , , and are all prime. My question is, can anyone disprove the claim that there are an infinite number of such primes.
The only progress I've been able to make is to show that must be of the form by considering the system of modular inequalities