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2016-04-08, 20:52   #11
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

31×317 Posts

Quote:
 Originally Posted by science_man_88 ... x must already be of a certain form for 6x-1 or 6x+1 to be composite so prove infinitely often that these forms are not met ?
In addition to what Charles wrote, infinitude of composite members of any sequence has nothing to do with the infinitude of prime members.

sm88, you need to start thinking at least about the basic properties of infinities: that is, (even for complementary sets, e.g. a set "A" and a set of all others "non-A"):
- a sum of a finite set and and infinite set is an infinite set;
- a sum of an infinite set and and infinite set is an infinite set, so
- knowing that one subset is infinite (e.g. "non-A") gives you no information about its complement's infinitude.