Patterns /Number Theory

Perfect Squares

A perfect square is some whole number times itself: 144 = 12², 10000 = 100². The range ends neatly on 1,000,000 = 1000².

Matches in range
1,001
Share of all numbers
1 in 999
Out of
1,000,001

Squares thin out in the most visible way of any trait here: the gap between consecutive squares grows steadily, so their density falls like 1 / (2√n). Only about a thousand exist below a million, as the count above confirms.

That makes a perfect square a substantially stronger claim than being prime, despite squares feeling more familiar — a good demonstration of why RNGdle scores from measured frequency rather than intuition.

Squares also interact with the digit patterns: a square that is also a palindrome, like 698896, is genuinely exceptional, and several such numbers rank near the top of the leaderboard.

Highest-scoring examples

The best-scoring numbers of four digits or more that carry this pattern. Shorter numbers are excluded here because their length alone dominates any score ranking.

Smallest examples

The first numbers in the range that match this pattern.

Related number theory patterns