Last Digit of Perfect Numbers Alternates between 6 and 8

Conjecture
The last digit of the sequence of perfect numbers alternates between $6$ and $8$:
 * $6$
 * $28$
 * $496$
 * $8128$

Refutation
The sequence continues:
 * $33 \, 550 \, 336$
 * $8 \, 589 \, 869 \, 056$

... two consecutive perfect numbers ending in $6$.

Also see

 * One Perfect Number for Each Number of Digits
 * Perfect Number ends in 6 or 28 preceded by Odd Digit