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Subtract the last digit from the rest. The result must be divisible by 11. 627: 62 − 7 = 55 = 5 × 11. Add 10 times the last digit to the rest. The result must be divisible by 11. (Works because 99 is divisible by 11). 627: 62 + 70 = 132: 13 + 20 = 33 = 3 × 11. If the number of digits is even, add the first and subtract the last digit from ...
Two properties of 1001 are the basis of a divisibility test for 7, 11 and 13. The method is along the same lines as the divisibility rule for 11 using the property 10 ≡ -1 (mod 11). The two properties of 1001 are 1001 = 7 × 11 × 13 in prime factors 10 3 ≡ -1 (mod 1001) The method simultaneously tests for divisibility by any of the factors ...
This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. [2] ... 2 3 5 7 11 13 17 19 23 29
This is because if you do this alternating sum calculation for a number you can use the result to test the divisibility for 7, 11 and 13 all in one calculation. Also, for whatever it's worth, in general for 11, you can do the alternating sum on any odd sized blocking and the simple addition on any even sized blocking.
A prime divides if and only if p is congruent to ±1 modulo 5, and p divides + if and only if it is congruent to ±2 modulo 5. (For p = 5, F 5 = 5 so 5 divides F 5) . Fibonacci numbers that have a prime index p do not share any common divisors greater than 1 with the preceding Fibonacci numbers, due to the identity: [6]
Since n must be at least 13, the primorial must be at least 1·2·3·5·7·11·13, and 7×11×13 = 1001. Fuller also refers to powers of 1001 as Scheherazade numbers. The smallest primorial containing Scheherazade number is 13# = 30,030. Fuller pointed out that some of these numbers are palindromic by groups of digits.
For example, since 19 divides a 11 and 2 × 19 = 38 does not divide 11, so 19 divides a 18k+11 for all k. Thus, the definition of irregular pair ( p , n ) , n should be at most p − 2 . The following table shows all irregular pairs with odd prime p ≤ 661 :
A sanity test can refer to various orders of magnitude and other simple rule-of-thumb devices applied to cross-check mathematical calculations. For example: If one were to attempt to square 738 and calculated 54,464, a quick sanity check could show that this result cannot be true. Consider that 700 < 738, yet 700 2 = 7 2 × 100 2 = 490,000 ...