Is this obvious? Starting with the third prime "5",
a prime is less than the product of all preceding primes plus 1 .
A few examples seem convincing that the statement is true, but I have not been able to demonstrate it.
Yes it's true. Google "Bertrand's Postulate", so that if we have the prime p and p' is the prime before it, then p < 2p'...
And so, in fact, your statement could very seriously be strengthened: every prime >= 3 is less than the prime before it times the first prime.
No, not obvious, but pretty straigthforward for whoever knows BP.
Tonio
Thanks, Tonio and PaulRS! I shall look up Bertrand's Postulate, Tonio.
PaulRS: Yes, now that I have your reply, I see the simplicity I was not able to conger. G.E. Andrews, in his "Number Theory" states the inequality in a hint towards the solution of an exercise, but I could not demonstrate the hint - let alone the entire exercise!
Thanks to you, both. Now, I can struggle on.
Nivla.