Steven G Elite Member Joined Dec 30, 2014 Messages 14,603 Nov 20, 2023 #1 Show that there are no arithmetic progressions, a, a+1b, a+2b, ...,that contain solely prime numbers.
Show that there are no arithmetic progressions, a, a+1b, a+2b, ...,that contain solely prime numbers.
lev888 Elite Member Joined Jan 16, 2018 Messages 2,993 Nov 20, 2023 #2 Steven G said: Show that there are no arithmetic progressions, a, a+1b, a+2b, ...,that contain solely prime numbers. Click to expand... Spoiler a+ab can't be a prime.
Steven G said: Show that there are no arithmetic progressions, a, a+1b, a+2b, ...,that contain solely prime numbers. Click to expand... Spoiler a+ab can't be a prime.
Steven G Elite Member Joined Dec 30, 2014 Messages 14,603 Nov 20, 2023 #3 Now show that a, a+1b, a+2b, .... must contain infinitely many composite numbers.
lev888 Elite Member Joined Jan 16, 2018 Messages 2,993 Nov 20, 2023 #4 Steven G said: Now show that a, a+1b, a+2b, .... must contain infinitely many composite numbers. Click to expand... Spoiler a+(a^k)b
Steven G said: Now show that a, a+1b, a+2b, .... must contain infinitely many composite numbers. Click to expand... Spoiler a+(a^k)b
