A few thoughts...
personally I LIKE 13, but
There is on a Scottish Mason's apron seven tassels on each side.
In almost every system of antiquity there are frequent references to the number seven.
The Pythagoreans called it the perfect number, 3 and 4, the triangle and the square, the perfect figures.
There were for instance seven ancient planets. The sun was the greatest planet of the ancient seven and next to the sun, the moon, changing in all its splendor every seventh day.
The Arabians had seven Holy Temples.
In Persian mysteries there were seven spacious caverns through which the aspirants had to pass.
The Goths had seven deities, as did the Romans, from whose names are derived our days of the week.
In Scriptural history there is a frequent recurrence to this number. E.g. in Revelation 1:16 -- "and He had in His right hand seven stars, " alluding to the seven churches of Asia.
For Masons, King Solomon was seven years building the Temple. It was dedicated to the glory of God in the seventh month and the festival lasted seven days.
There are seven liberal arts and sciences.
Masons require seven Brethren to make a Lodge perfect and they have our seven steps on the winding staircase.
It seems that every culture has lucky numbers and unlucky numbers. In Japan, four and nine are considered as unlucky numbers because of their pronunciation. Four is pronounced "shi" which is the same pronunciation as death. Nine is pronounced "ku" which has the same pronunciation as agony or torture.
7 wonders of the world combined with the 7 deadly sins...
Just some possibilities...Q