To further answer your question. If you look in the documentation for NSNumber's isEqualToNumber: function you will notice the following line,
Two NSNumber objects are considered equal if they have the same id values or if they have equivalent values
it's important you understand this. In your code you are asking is my NSNumber object "number" equal to "value", you are not asking does the numerical value stored within my NSNumber object "number" equal the numerical value stored within my NSNumber object "value".
The last line of code you have written shows that in fact your NSNumber's numerical values are in fact equal.
NSLog(@"%d", [number unsignedLongLongValue] == value); //1
So you are correctly storing and retrieving the values, you should be using the == comparison method with NSNumber objects stored numerical values (ie intValue == intValue, unsignedLongLongValue == unsignedLongLongValue) and not comparing their object id's together.
As for this line of code
NSLog(@"Current Number:%@", number); // -2538698204676668398, weird
This is not weird, this is perfectly normal, as you have told NSLog to print out an NSObject representation of 'number'. I'm not 100% certain but I believe that NSNumber's - ( NSString * ) description
function defaults to return an unsigned int value for the numerical value it contains. This is why you are getting the large negative number returned. You may want to look at NSNumber's - (NSString *)descriptionWithLocale:(id)aLocale
function to print out the data in a more logical for for you, or you could use
NSLog(@"Current Number:%llu", [number unsignedLongLongValue]);
Which will give you the right answer.
EDIT:
Further to this, after looking into the issue what is happening is that on recollection of your NSNumber object from UserDefaults it's original number type is not being preserved (this information is highlighted in the documentation for NSNumber in the overview section)
(Note that number objects do not necessarily preserve the type they are created with.)
You can see this yourself if you log the following after retrieving "number" from user defaults (add this to the end of the code you have in your question) and have a look at the encoding values shown here
NSLog(@"%s", [number objCType]); //This will log out q
NSLog(@"%s", [[NSNumber numberWithUnsignedLongLong:value] objCType]); //this will log out Q
The difference between Q and q is that Q is an unsigned value... hence why you are having issues with the isEqualToNumber: function as the number types are different.
If you are so dead set on using the iSEqualToNumber: function to compare values then you could implement this to retrieve your value from NSUserDefaults.
NSNumber *number = [NSNumber numberWithUnsignedLongLong:[[NSUserDefaults standardUserDefaults] objectForKey:NumberKey] unsignedLongLongValue]];
You could look at using the NSNumber compare: function to see if the returned value is NSOrderedSame however this will not work for comparing unsigned vs signed values of the same type so in your situation I'd use the above as retrieving the data from NSUserDefaults is stripping the "signedness" of your number.