What is the shortest way to write the number $1234567890$?
WEBHere's a challenge : find the shortest way to write the number 1234567890 1234567890 . There is several ways to write the number 1234567890 1234567890 : 1.23456789 ×109 1.23456789 × 10 9. 2 ×32 × 5 × 3607 × 3803 2 × 3 2 × 5 × 3607 × 3803. 617283945 × 2 617283945 × 2. But all these notations are longer. Can you find a shorter ...
Primes made from sequential digits - Mathematics Stack Exchange
WEBFor all numbers consisting of n n digits, there are at most 4 consecutive digit primes, since the last digit must be 1, 3, 7 1, 3, 7 or 9 9. The number of n n digit primes, in the limit of large n n, should scale as 9×10n ln10n 9 × 10 n ln. . 10 n, by the prime-number theorem. Thus we might expect that the asymptotic density of consecutive ...
How to prove that $x=0.1234567891011\\dots $ is irrational?
WEBThe decimal representation of a rational ends by repeating the same digits periodically. The number 0.1234567891011… includes arbitrarily large sequences of zeroes (it inculdes 10, 100, 1000, 10000, ...). But it also includes arbitrarily large sequences of 1's (it includes 1, 11, 111, 1111, ...). This is contradictory with the fact that it ...
probability - prove 0.1234567891011... is a normal number
WEBJun 28, 2019 · Prove that 0.123456789101112... is normal. So the number of times 1 appear in the first 9 digits after the decimal point is 1, then in the next 90 digits is 19 = 10 + 1 + 8 ∗ 1, then the number of times 1 appears in the next 900 digits is 100 + 19 + 19 ∗ 8... Here is what I tried:So if we look at the first 10i digits after the decimal ...
Whether there is a prime in sequence - Mathematics Stack Exchange
WEBMar 31, 2021 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Is there any deep reason that 23456789 is prime? [closed]
WEBOct 9, 2017 · As posed, I would say that the answer to your question is no. Say we are given just a single positive integer n, in your question n = 23456789. In this case there is no "deep reason" for n to be prime. Either n is prime or not, it is what it is. On the other hand, suppose we are given a random integer 1 ≤ n ≤ N.
Find the minimum natural number - Mathematics Stack Exchange
WEBFeb 26, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Why is $\\frac{987654321}{123456789} = 8.0000000729?!$
WEBMay 20, 2013 · 19. 98765432 / 12345679 = 8, exactly. You can see how the pattern works by multiplying out 12345679 ∗ 8 starting at either end. This explains why your fraction is close to an integer. If you think the 729 is interesting (I don't), it can be explained by some of the other answers here.
Questions about primes made from consecutive numbers starting …
WEB1. Similar to: Does there exist a prime that is only consecutive digits starting from 1? Let bn = a1a2a3 …an¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ b n = a 1 a 2 a 3 … a n ¯ and an = n a n = n. For example b11 = 1234567891011 b 11 = 1234567891011. I have a couple of questions about the primes in the sequence bn b n. What is ...
Show that any set of 7 distinct integers includes two integers
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