Resumen de On the Probability That Two Random Integers Are Coprime

Jing Lei, Joseph B. Kadane

• We show that there is a nonempty class of finitely additive probabilities on N2 such that for each member of the class, each set with limiting relative frequency p has probability p. Hence, in that context the probability that two random integers are coprime is 6/π2. We also show that two other interpretations of “random integer,” namely residue classes and shift invariance, support any number in [0,6/π2] for that probability. Finally, we specify a countably additive probability space that also supports 6/π2.