The century rule is where simple "divisible by 4" checks go wrong. Enter 1900: it divides by 4 (475) and by 100 (19) but not by 400 (4.75), so the calculator returns No, 365 days, and reports 1896 as the previous leap year and 1904 as the next. Now enter 2000: it divides by 4, by 100 and by 400 exactly (5), so it returns Yes, 366 days, with 1996 before it and 2004 after it. Two years that look identical to a divide-by-4 test land on opposite sides of the rule.
The same rule produces the longest wait anyone alive today is likely to see for a February 29. Suppose you are planning from a date in 2097 and want the next leap year. Enter 2097: the previous leap year is 2096, but the next one is 2104, not 2100, because 2100 is a century year that fails the 400 test. With the look-ahead at 20 years, the upcoming list reads 2104, 2108, 2112 and 2116. Enter 2096 itself and the list reads 2096, 2104, 2108, 2112, 2116, showing an eight-year gap where you would normally expect four.
Any schedule, subscription or contract that assumes "every fourth year" will be off by one leap day in 2100. That is why software should call a real leap-year test rather than checking year mod 4 alone.