Exploring Mersenne primes 2^p -1

Just a note:
My app "Touch Integers ℤ (+ - × ÷)" is useful to explore the Mersenne primes:
Here there's a tiny exploration from 2^2 -1 to 2^23 -1.
We found all numbers prime, except when p==11 and p==23
Like everybody knows:

The search is made with:  "Touch Integers ℤ (+ - × ÷)" Android app:

https://play.google.com/store/apps/details?id=com.nummolt.touch.integers

http://www.nummolt.com

///////     UPDATE:  (August 2016)    ////////

Same exploration on Wagstaff Prime Numbers:  

 

 Woodall Primes:

 

     

Euler's Lucky numbers:

 

   

And Goldbach's Conjecture:

 
 

The exploration has been made with:  "Touch Integers ℤ (+ - × ÷)" Android app:

https://play.google.com/store/apps/details?id=com.nummolt.touch.integers

http://www.nummolt.com

Touch decimals. Part 5. Collaboration

The 07/04/2015 after some days from the first post of "Touch decimals":
https://play.google.com/store/apps/details?id=com.nummolt.math.value.place 
I received this animation from JeffL (member of MathTools & author of: 
"Jeff's Interactive K12 Math Scripts Page") :

http://www.nummolt.com/LeMieux.gif 

This led me to develop an alternative program with its version.
And I added it to my original program.
With translation between the two systems.
(One with 'Tokens' signed and  'Places' unsigned, and the other with color
'Tokens'  unsigned and 'Places' signed).
I think the program has been enriched by the two visions.

The pre-release videos:

Borrowing in subtraction

Borrowing in subtraction and the color of Tokens

Transition between the two methods

The YouTube Video about the posted version (July 15 2015): Touch decimals v.1.1.0 r.4:

Touch decimals promotional video

I should also like to thank Wendy Petti for comments made in the early development of this program.

From 2015/09/1 There's a online version of "Touch decimals Place value"  JavaScript version:

www.nummolt.com/touchdecimals/index.html 

Touch decimals: Part 4: Borrowing in subtraction. Carry in Addition.

Touch decimals Place value ±

Borrowing in subtraction:

Carry in addition:

MERGED 2016/11/10:

And from a dialog on Twitter: https://twitter.com/macajo/status/793790918788837376

The following Video:  Subtraction: 534-486:

 

Touch decimals Part 3: Basic interaction

Touch decimals,Place value ±

Basic interactions:

Video:

Touch decimals: Part 2: Tokens and Places

New: Touch decimals: free Android app: Part II

Touch decimals,Placevalue ±

Main components of Touch Decimals:

The main board with two charts of identic number of inner rectangles.

Each chart with:

A number with dot that represents each one of the two numbers.

A button to change the sign of all the inner components of each chart.

A row of a variable number of rectangles named: “Places”

A variable number of big dots (with numbers inside), named: “Tokens”.

In the “settings” button or option button: the way to refresh the charts.

PLACES:

A place is a rectangle, and a rectangle has 4 borders:

The top and bottom border may limit another equivalent place, or an abyss where can fall tokens, and become lost forever.

A token is free to cross any of those boundaries under its responsibility.

The left border is impenetrable:

Only it is authorized by the passage of a token if it gets the support of 10 tokens of the same type.

When the 10 tokens have crossed the left border, become one token

The right border:

Right border can be crossed freely

If a token cross the right boundary, it becomes 10 tokens of the same type in the next place.

The maximum reccomended number of tokens into each place is: nine.

TOKENS:

A token can be either positive or negative

A positive token is born with the tap of a finger on the screen

A pair of positive-negative tokens is born with a tap of two fingers on the screen

A token disappears if it crosses the top or bottom border.

Positive and negative tokens have the same behavior:

A token can cross at will the intermediate horizontal border

When a token crosses the border on the right, it becomes 10 tokens.

A token need 9 companions from the old place to cross the border to the left.

Positive and negative tokens may be in the same place. 

But if two tokens of different signs meet, they cancel each other.

Touch decimals,Place value ±

This is how the tokens live in their places in "Touch decimals, Place value ±"

The behavior of places and tokens of this app describes the behavior of the numbers in the decimal system.

Development:

All in this text: charts (twins), places and tokens also describes the internal structure of the app and his internal java classes:

Touch decimals: Part 1: References

New Touch decimals: free Android app: Part I

Touch decimals,Place value ±

Introduction:

This is the application with a longer history among which I developed in www.nummolt.com.

The first version, made after two failed attempts was published in 1997:

I named it nummòlt, and in fact was the fundational application of nummolt.com.

Nummòlt was a application developped in C ++, and it was my first OOP program:

(Old nummòlt download page)

It was one of many attempts in the nineties to represent numbers graphically to kids.

I will like to remember some of the contemporaries who tried to represent numbers graphically:

Jacobo Bulaevsky: and www.arcytech.org page:

(Rebuilt by Jill Britton and Suzanne Alejandre of MathForum)

http://britton.disted.camosun.bc.ca/baseten/instructions.html

http://mathforum.org/varnelle/howto.html

http://britton.disted.camosun.bc.ca/patterns/patterns_d.html

(Jacobo Bulaevsky died in 8/13/2004)

(Base Ten Instructions)

Brian Sutherland and his: our-montessori.com:

http://web.archive.org/web/20060113011625/www.our-montessori.com/home.html

A rebuild of the Original:

http://www.our-montessori.ca/

http://ethereal.utm.utoronto.ca/our-montessori/math/stampgame.php(needs Shockwave player ')

http://ethereal.utm.utoronto.ca/our-montessori/math/largebeadframe.php(needs Shockwave player ')

(Stamp game)

In collaboration with Wendy Petti of MathCats, in 2003 we did the "Place Value Party"

http://www.mathcats.com/explore/age/placevalueparty.html

With the "place value" shaped as floors of a virtual birthday cake:

(MathCats.com Place Value Party)

In recent years, with the advent of affordable graphic tablets, there are new approaches:

Mainly: Ulrich  Kortenkamp (The creator of Cinderella). The Place Value Chart

https://itunes.apple.com/us/app/place-value-chart/id568750442

(Kortenkamp: Place Value Chart: iTunes)

(Here I must recommend the book: "Early Mathematics Learning: Selected papers of the POEM 2002 Conference": https://books.google.es/books?id=Lui3BAAAQBAJ ) 

And also:
Christian Urff: Rechentablett:

https://itunes.apple.com/de/app/rechentablett/id574825573

(Urff: Rechentablett: iTunes)

After the appearance of all this, I saw the possibility of bringing my previous programs under the way to represent numbers used by Urff and Kortenkamp.

This is my free: "Touch decimals, Place value ±" for Android.

Place value structure seen before, adding tokens with sign, and with the ability to create the neutral element of the sum: pairs of tokens positive - negative that do not alter the final outcome of any addition or subtraction operation.

https://play.google.com/store/apps/details?id=com.nummolt.math.value.place

(Nummolt's Touch decimals,Place value ±)

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