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As a biprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0); it is the second composite number with an aliquot sum of 11, following 18. 21 is the first member of the second cluster of consecutive discrete semiprimes (21, 22), where the next such cluster is (33, 34, 35).
Since Number Sense is designed to test students' mental math abilities, no calculators or scratch paper can be used during competition. In order for a question to be scored as correct the exact answer must be given (no allowance for rounding), except where the question is preceded by an asterisk, in which case for the question to be scored as ...
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters. 89
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
Prohibiting calling out a series of numbers that sum to 21 (e.g. "6, 7, 8" or "10, 11") Examples of new rules that could be instated by a player forced to call 21: Swapping two numbers around (e.g. 3 and 13 are switched) Replacing a number with a humorous phrase (e.g. replacing 5 with "skin" - causing the sequence 1, 2, 3, "foreskin")
Thus, all Mersenne numbers M 4k +1 are congruent to 11 modulo 20 and end in 11, 31, 51, 71 or 91, while Mersenne numbers M 4k −1 ≡ 7 (mod 20) and end in 07, 27, 47, 67, or 87. For the perfect numbers, define P n = 2 n−1 M n be the value which is perfect if M n is prime.