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All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical digits and a fourth digit that is one higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 ...
Trachtenberg system. The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian engineer Jakow Trachtenberg in order to keep his mind occupied while being in a Nazi concentration camp.
The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8 = 9. The multiplicative persistence of 39 is 3, because it takes three steps to reduce 39 to a single digit: 39 → 27 → 14 → 4. Also, 39 is the smallest number of multiplicative persistence 3.
All examples use example date 2021-03-31 / 2021 March 31 / 31 March 2021 / March 31, 2021 – except where a single-digit day is illustrated. Basic components of a calendar date for the most common calendar systems: D – day; M – month; Y – year; Specific formats for the basic components: yy – two-digit year, e.g. 24; yyyy – four-digit ...
As an example, starting with the number 8991 in base 10: 9981 – 1899 = 8082 8820 – 0288 = 8532 8532 – 2358 = 6174 7641 – 1467 = 6174. 6174, known as Kaprekar's constant, is a fixed point of this algorithm. Any four-digit number (in base 10) with at least two distinct digits will reach 6174 within seven iterations. [1]
The product of two variables ranging from 90-99 will result in a 4-digit number. The first step is to find the ones-digit and the tens digit. Subtract both variables from 100 which will result in 2 one-digit number. The product of the 2 one-digit numbers will be the last two digits of one's final product.
Either group the thousands in a four-digit number or do not, but not mixed use in the same article. However, grouping by threes and fives may coexist. Four-digit page numbers and four-digit calendar years should never be grouped (not sailed in 1,492, but dynasty collapsed around 10,400 BC or by 13 727 AD, Vega will be the northern pole star).
Primes that are not the sum of a smaller prime and twice the square of a nonzero integer. 2, 3, 17, 137, 227, 977, 1187, 1493 (OEIS: A042978) As of 2011, these are the only known Stern primes, and possibly the only existing.