Not all values between U+11111 and U+22222 are defined in the Unicode standard (compare http://www.unicode.org/Public/6.2.0/ucd/UnicodeData.txt), therefore I take a different range as an example:
uint32_t first = 0x1F300;
uint32_t last = 0x1F310;
NSMutableString *string = [NSMutableString string];
for (uint32_t unicode = first; unicode <= last; unicode++) {
// Create a string from the (4 byte, little-endian) unicode value:
NSString *tmp = [[NSString alloc] initWithBytes:&unicode length:4 encoding:NSUTF32LittleEndianStringEncoding];
[string appendString:tmp];
}
NSLog(@"%@", string);
Output: 🌀🌁🌂🌃🌄🌅🌆🌇🌈🌉🌊🌋🌌🌍🌎🌏🌐