101
This number is a prime.
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The 5th centered decagonal number (numbers of the form 5(n^2 - n) + 1). [Green]
Something 101 (pronounced 'one-oh-one') in popular slang is the beginning or introductory lessons required for any understanding, as in 'Home Buying 101' or 'Prime Numbers 101'. [Green]
101 (base b) is a near-square number in every base b and it is conjectured that there are infinitely many bases for which 101 is prime. [Green]
POWERS OF 101 - PASCALINDROMES | |
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The first five consecutive powers of 101 produce palindromes. The next 4 consecutive powers of 101 produce 'quasi-palindromes' in the sense of concatenating several multidigit numbers in reverse order, but not reversing the digits of those individual numbers. In all these powers the numbers in the rows of Pascal's Triangle can be seen in order (with some zeros thrown in here and there so that each number, after the first, occupies a two-digit space), hence the name 'Pa-sca-lindromes'. |
101^{0} = 1 101^{1} = 101 101^{2} = 10201 101^{3} = 1030301 101^{4} = 104060401 101^{5} = 10510100501 101^{6} = 1061520150601 101^{7} = 107213535210701 101^{8} = 10828567056280801 |
(There is one curio for this number that has not yet been approved by an editor.)
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