Blue Moons - frequency by month

Do Blue Moons occur more frequently in some months than others? We looked at all of the Blue Moons for 10,000 years starting with the year 1600, and this is what we found:
Month Full Moons on
1st and 30th
Full Moons on
1st and 31st
Full Moons on
2nd and 31st
Total
January 156 202 128 486
February 0
March 137 220 119 476
April 147 147
May 169 165 157 491
June 161 161
July 163 179 162 504
August 178 165 168 511
September 181 181
October 174 161 181 516
November 162 162
December 151 199 144 494
The months with 31 days are clearly more likely to have two Full Moons than those with just 30 days. February never sees two Full Moons, because the minimum interval between Full Moons is always greater than the length of that month, even in a leap year.
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