Computed with engine art-1.0.0. Data updated: 2026-09-26 (UTC). Rules independently implemented by RNGDLE.ART.
Encodings
Rule, exact count and rarity
A binary palindrome reads the same in both directions when written in base two without leading zeros. The representation must contain at least two bits, so the single-bit values 0 and 1 are excluded by this badge's convention. Since every nonzero binary representation starts with 1, a qualifying palindrome must also end with 1 and therefore be odd. Decimal and binary symmetry are separate tests: neither implies the other. For example, the decimal integer 9 is 1001 in binary and satisfies this rule despite having only one decimal digit. Binary all-ones numbers automatically qualify as binary palindromes, but the two representation signals overlap and receive discounted contributions within their scoring family.
The exact count, 1,998, comes from evaluating all 1,000,001 integers from 0 through 1,000,000, including both endpoints. It is not a sample or an estimate. Each matching integer is counted once for this category, even if it contains multiple qualifying segments. Its frequency of 0.1998% describes the chance that a uniformly chosen integer passes this one test. It is not the global score percentile of every member, and overlapping pattern counts must not be added as if they represented disjoint sets.
The pattern supplies −log₂(1,998 / 1,000,001) bits before its within-family weight is applied. Other matched patterns, digit sum, distinct-digit count and short-length signals can change the complete score. Consequently, members of this category need not share a ranking. The highest-scoring representative is 3, with a rarity score of 1,677 and Top 0.0001%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.
Example numbers
ExploreThe highest-scoring match
The highest-scoring representative is 3, with a rarity score of 1,677 and Top 0.0001%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.
Frequently asked questions
How many binary palindrome numbers are there between 0 and 1,000,000?
There are exactly 1,998 matches for binary palindrome numbers among the 1,000,001 integers from 0 to 1,000,000, inclusive: 0.1998% of the range. At least two binary digits read the same in reverse.
Can an even positive integer be a binary palindrome?
Not under the unpadded multi-bit rule. An even binary integer ends in 0 but begins in 1, so its first and last bits cannot match.
What is the highest-scoring binary palindrome numbers representative?
The highest-scoring representative is 3, with a rarity score of 1,677 and Top 0.0001%. This uses its complete score across all features, not just this pattern. Equal scores are displayed in ascending numerical order.