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1. Puzzle 59.- Six and the nine digits primes (by Jud McCranie)
- www.primepuzzles.net
- - Six and the nine digits primes (by Jud McCranie).
- "Prove that every 9-digit prime (no leading zero) that has distinct digits.
- "Consider any 9-digit number with distinct digits. If this number does not contain the digit "6", then it is the other 9 digits (0,1,2,3,4,5,7,8,9) in some order. But the sum of these digits is 39, so this 9-digit number is divisible by 3. ... A similar argument can be used to show that these 9-digit primes also contain the digits 0, 3, and 9. ...
- I became interested in sequence A046732 (by our friend Enoch Haga) - primes with distinct digits whose reversal is also prime. There are obviously only a finite number of them, since any number with more than 10 digits can't have distinct digits. So I decided to find the largest member of the sequence, the total number of terms in the sequence, and the number with 1 digit, 2 digits,. ... 10 digits.
- I modified the program to not require that the prime be reversible - just that it had distinct digits. ...
- Next I wrote a program to generate all primes between 10^9 and 10^10 - and it showed no 10-digit primes with distinct digits! I checked that program and I couldn't find any error.
- I wrote a program to generate all n-digit numbers with distinct digits and test them for primality. ... Then I ran it for 10-digit numbers, and again - no 10-digit primes with distinct digits. ...
- I revised the program to test all 9-digit primes with distinct digits, and sure enough - each one had a "0"! This is amazing, I thought. ... I decided to check all digits on 9-digit primes with distinct digits. They all have the digits 0, 3, 6, and 9! Now it finally dawned on me. The sum of the digits 0 through 9 is 45; 45 is divisible by 3; so any number using each of the digits once and only once is itself divisible by 3 - hence not prime. And for 9-digit numbers with distinct digits, if 0, 3, 6, or 9 is avoided, the sum of digits is divisible by 3 so the number itself is divisible by 3. So any 9-digit prime with distinct digits must have 0, 3, 6, and 9; and there are no 10-digit primes with distinct digits. I could have saved myself a lot of trouble and excitement if I had stopped to think when I first saw that there seemed to be no 10-digit primes with distinct digits, but (naturally) I suspected an error in my program. ...
2. Function Float-Digits in theory Kif-Numbers
- www-ksl.stanford.edu
- Function FLOAT-DIGITS.
- Documentation: The term {tt (float-digits $tau$)} denotes the number of digits used in the representation of a floating point number denoted by $tau$. ...
3. Arithmetic/digits
- rec-puzzles.org
- Section Arithmetic/digits.
- Does every number which is not divisible by 5 have a multiple whose only digits are 6 and 7? Solution all. ...
- What is the Arabian Nights factorial, the number x such that x! has 1001 digits? How about the prime x such that x! has exactly 1001 zeroes on the tail end. ...
- What 6 digit number, with 6 different digits, when multiplied by all integers up to 6, circulates its digits through all 6 possible positions, as follows: ABCDEF * 1 = ABCDEF ABCDEF * 3 = BCDEFA ABCDEF * 2 = CDEFAB ABCDEF * 6 = DEFABC ABCDEF * 4 = EFABCD ABCDEF * 5 = FABCDE Solution cryptarithm.
- Find the least number using 0-9 exactly once that is evenly divisible by each of these digits. ...
- What are the extremal products of three three-digit numbers using digits 1-9? Solution labels.
- digits.
- Form a number using 0-9 once with its first n digits divisible by n. ...
- Prove that for any 9-digit number (base 10) there is an integral power of 2 whose first 9 digits are that number. ...
- Is there an integer that has its digits reversed after dividing it by 2? Solution rotate.
- Find integers where multiplying them by single digits rotates their digits one position, so that the last digit become the first digit. ...
- digits.
4. significant digits (counting significant digits)
- clouseau.chemistry.sjsu.edu
- Counting Significant Digits.
- Counting significant digits is as simple as 1-2-3. ...
- All non-zero digits and "trapped zeros" (zeros which occur between significant digits) are significant digits.
- Leading zeros are never significant digits. ...
- Trailing zeros to the right of the decimal are always significant digits. ...
- Then if the zeros are significant digits, it is clear because the occur as trailing zeros to the right of the decimal place.
- Conversion factors which are based on definitions (such as 1000 mL per L or 3600 seconds per hour) have an infinite number of significant digits (because they are exact. ...
- Some physical constants are so well determined that the number of significant digits can be chosen. An example of this is pi which can be used to 3 significant digits (3. ...
- 4 significant digits.
- 3 significant digits.
- 4 significant digits.
- 2, 3 or 4 significant digits.
- 3 significant digits.
- 4 significant digits.
- 4 significant digits.
5. Practice with Significant Digits
- homepages.ius.edu
- Significant Digits: Counting, Math operations and Measurement.
- These sites are useful for practice with counting the number of significant digits, math operation using significant digits, and making measurements using significant digits. ...
- Significant Digit Tutorial A tutorial dealing with measurement, uncertainty (uncertain digit) and significant digits. ...
- Significant Digits and Zeros When do you count zeros as significant? This page contains helpful hints. ...
6. DaqDataDecoding: CS::Chip::Digits Class Reference
- wwwcompass.cern.ch
- Main Page | Namespace List | Class Hierarchy | Alphabetical List | Class List | File List | Namespace Members | Class Members | File Members | Related Pages | Examples CS::Chip::Digits Class Reference.
- List of digits. ...
- Digits (void).
- ~Digits (void).
- Clear the digits list. ...
- Clear the digits list (the same as Clear()). ...
- Print all digits. ...
- List of digits. ...
- CS::Chip::Digits::Digits .
- CS::Chip::Digits::~Digits .
- void CS::Chip::Digits::clear .
- Clear the digits list (the same as Clear()). ...
- void CS::Chip::Digits::Clear .
- Clear the digits list. ...
- Referenced by clear(), and ~Digits(). ...
- void CS::Chip::Digits::Print .
7. www.geocities.com/Colosseum/Field/7738/headst_digits.txt
- www.geocities.com
- # #-----------------------------------------------------------------------------# TAB FOR DIGITS BY The HEADSTONES FROM THE ALBUM: SMILE AND WAVE TRANSCRIBED BY MATTHEW HANSEN This is a cool song from an awsome album. ... ) You play A5 about 8 times, G5 4 and D5 like 10 or something(fast) A5 G5 D5 e------------------- B------------------- G-----2---------7--- D-----2----5----7--- A-----0----5----5--- E----------3-------- chorus(?) riff: E--------------------------- B--------------------------- h - hammer on G-------------------------4- D--------------------4h6---- A-----4--4--2--4--4--------- E--0------------------------ Lyrics: INTRO 2X shame on you shame on you VERSE 1: C#m She's got the numbers man I got the digits Everybody knows there own Pulses Quickened A5 Don't know the essence well they've Gone and made a mess C#m Jimmy wanted pistols but he Shot em when he got em Pre-Chorus: A5 No 2 snow flakes are alike G5 D5 And niether are the seconds CHORUS 4X(no lyrics) VERSE 2: C#m Be happy when we're in public Don't know how we ever got by I've got it now I'm damaged I'm a discontinued line A5 Too busy gettin sick to close Anybody can see the flaws C#m Billy wanted depth Maybe shoulda checked his pockets PRE CHORUS CHORUS: yeah SOLO/BRIDGE(haven't figured it out yet) VERSE 3: same as first verse, except instead of playing the C#m chord, play the intro instead. ...
8. SPOILER C:
- www.mathematik.uni-bielefeld.de
- SPOILER C: - - - - - - - - - - - - - - - - - - - - - - - - - - - ==> arithmetic/digits/squares/three. digits. s <== puzzles-faq/part03 What square consits entirely of three digits (e. ...
9. Significant Digits
- www.gp.uwo.ca
- Significant Digits .
- The reported value of any measurement should adhere to the correct number of significant digits, which depend on the precision of a measurement. ... A reported measurement should contain all of the digits that are known with certainty, plus one more which is an estimate. ... The number of significant digits in this case is three. ...
- The digits 1 through 9 are always significant. ...
- a) they occur between two significant digits;.
- Multiplication or division should be rounded off to the number of significant digits in the least precise term used in the calculation. ...
- 0745 should be reported as 92, since the least precise term in the calculation has two significant digits. ...
- If a calculation produces a result with more significant digits than required, the following rules should be used to round off the number: .
- 00×102 is the same as 600 (three significant digits). ...
10. Sum-of-Digits Iterations
- www.mathpages.com
- Sum-of-Digits Iterations .
- Given a positive integer n, let s_B(n) denote the sum of the base-B digits of n. ... We will say that n "reduces to" r_B(n) under iteration of the sum-of-digits function. ... ) = s_B(n) (mod B-1) Therefore, the sum-of-digits function is the identity function modulo B, and so are iterations of this function. ... Thus, for each additional carry, the sum of digits is reduced by B-1 . ... What is the period of the reduced values of T n for the base B? We have T n = n(n+1)/2, and we know that two numbers reduce to the same single digit (under repeated summing of their digits in base B) if and only if they are congruent modulo B-1. ... Here are the cycles for the bases from 2 to 16 (using hex for the digits): B --- 2 1 3 1 1 2 2 4 1 3 3 5 1 3 2 2 3 1 4 4 6 1 3 1 5 5 7 1 3 6 4 3 3 4 6 3 1 6 6 8 1 3 6 3 1 7 7 9 1 3 6 2 7 5 4 4 5 7 2 6 3 1 8 8 10 1 3 6 1 6 3 1 9 9 11 1 3 6 A 5 1 8 6 5 5 6 8 1 5 A 6 3 1 A A 12 1 3 6 A 4 A 6 3 1 B B 13 1 3 6 A 3 9 4 C 9 7 6 6 7 9 C 4 9 3 A 6 3 1 C C 14 1 3 6 A 2 8 2 A 6 3 1 D D 15 1 3 6 A 1 7 E 8 3 D A 8 7 7 8 A D 3 8 E 7 1 A 6 3 1 E E 16 1 3 6 A F 6 D 6 F A 6 3 1 F F Return to MathPages Main Menu .
11. Difficult Digits
- www.olemiss.edu
- Difficult Digits.
- Arrange the digits 1,2,3,4,5,6,7,8,9,0 using only one operation sign so that they will equal 100. ...
12. Letters standing for digits
- magma.maths.usyd.edu.au
- Letters standing for digits.
- In what follows, digits have been consistently replaced by letters, with different letters being used for different digits: .
- We construct all the possibilities for ONE explicitly, by finding those squares in the range 100 to 999 whose digits are distinct. ...
- Slower Algorithm: The digits TFoptions for {T, F} will be chosen as a subset of size 2 from the set of non-zero digits with ONEchoice removed (this set has size 6). The digits WHRUoptions for {W, H, R, U} will be chosen as a subset of size 4 from the set of all digits with the digits for ONEchoice and TFchoice removed (this set has size 5). ... Note that the total number of choices of digits considered under this scheme is > 13 * Binomial(6, 2) * Binomial(5, 4) * Factorial(2) * Factorial(4); 46800 .
- Faster Algorithm: The reason that the above algorithm is slow is that it constructs all possible choices of digits such that ONE works, and then tests everything. It would be improved if the choice for TWO were tested before digits were allocated to THREE and FOUR, and similarly if the choice for THREE were be tested before digits were allocated to FOUR. ...
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