Magic Numbers: Integers

Josh Poley

Microsoft Corporation

Introduction

In testing software, we often miss an entire class of bugs just because we don't happen to think about one category of inputs and how they might adversely affect the system. To help combat this in with my own tests, I've pulled together a listing of numbers which are good to use in testing for various independent reasons.

At the very least, here are some free numbers which you can stick into your tests; pick the ones that make sense and add them to your regression tests. But better yet, you can use some of these numbers as a brainstorm to help spurn ideas about other classes of values to test in your application. To give you a brief sample, here are some of the categories covered here:

• Common character values
• Common boundaries
• Times and dates
• Colors
• Security - We cover values that often lead to overflow attacks, as well as characters used in cross site scripting and SQL injection attacks.
• Primes - Prime numbers are good because they can't be divided up nicely.

You may also want to treat the below numbers as boundaries themselves. Depending on your application it might make sense to not only supply the value listed here, but also add or subtract 1 from the number.

8 bit Integers (0 - 255)

Value	Hex	Description
0	0x00	Zero. False. Terminating NULL character.
1	0x01	One.
2	0x02	Two.
3	0x03	Prime.
4	0x04	Four. Size of a 32 bit integer or pointer. 2^2.
5	0x05	Five fingers. Prime.
7	0x07	2^3 - 1. Largest single digit octal value. Seven days in a week. Prime.
8	0x08	2^3.
10	0x0A	Humans usually think in decimal, so arrays, lists, etc. are often a multiple of ten.
15	0x0F	2^4 - 1. Largest single digit hexadecimal value.
16	0x10	2^4.
24	0x18	Hours in a day.
32	0x20	2^5.
34	0x22	Numerical value for the double quote ASCII character which is often used in cross site scripting attacks.
37	0x25	Numerical value for the ASCII character '%' which is an escape sequence in URLs and the C run time library.
38	0x26	Numerical value for the ASCII character '&' which is often used in cross site scripting attacks.
39	0x27	Numerical value for the single quote ASCII character which is often used in cross site scripting attacks.
42	0x2A	Aside from a book/movie reference, developers often use this as an arbitrary value.
48	0x30	Numerical value for the ASCII character '0' (zero).
52	0x34	Number of weeks in a year.
59	0x3B	Numerical value for the ASCII character ';' which is often used in SQL injection and cross site scripting attacks.
60	0x3C	Number of seconds in a minute. Number of minutes in an hour. Numerical value for the ASCII character '<' which is often used in cross site scripting attacks.
62	0x3E	Numerical value for the ASCII character '>' which is often used in cross site scripting attacks.
64	0x40	26.
65	0x41	Numerical value for the ASCII character 'A'. 2^6 + 1.
85	0x55	Repeating "01" bit pattern.
90	0x5A	90 degrees.
97	0x61	Numerical value for the ASCII character 'a'.
99	0x63	Two nines. Largest 2 digit value.
100	0x64	100.
127	0x7F	2^7 - 1. The maximum signed 8 bit value. Largest 7 bit prime. Last character in the standard ASCII character map.
128	0x80	2^7.
170	0xAA	Repeating "10" bit pattern.
204	0xCC	x86 assembly instruction, if executed, halts the process ("int 3").
251	0xFB	Largest 8 bit prime.
255	0xFF	The maximum unsigned 8 bit value (2^8 - 1). Maximum filename length on several common file systems. Blue in a 24 bit RGB format.

Raw List

0, 1, 2, 3, 4, 5, 7, 8, 10, 15, 16, 24, 32, 34, 37, 38, 39, 42, 48, 52, 59, 60, 62, 64, 65, 85, 90, 97, 99, 100, 127, 128, 170, 204, 251, 255

16 bit Integers (256 - 65,535)

Value	Hex	Description
256	0x0100	2^8.
257	0x0101	2^8 + 1.
260	0x0104	MAX_PATH.
360	0x0168	Number of degrees in a circle.
365	0x016D	Number of days in a year.
512	0x0200	2^9.
1000	0x03E8	Number of milliseconds in a second.
1024	0x0400	Kilobyte. 2^10.
1601	0x0641	Year when time started according to the Windows FILETIME format.
1970	0x07B2	Year when time started according to the CRT time_t format.
1999	0x07CF	Just before Y2K.
2004	0x07D4	A leap year.
2100	0x0834	Year divisible by four but is not actually a leap year.
3600	0x0E10	Number of seconds in an hour.
4095	0x0FFF	2^12 - 1.
4096	0x1000	4k. 2^12. Size of a page of memory on Windows. Common file system cluster size.
4097	0x1001	2^12 + 1.
9999	0x270F	Four nines. Largest value under 10000.
16383	0x3FFF	2^14 - 1.
16384	0x4000	16k. 2^14. Common file system cluster size.
16385	0x4001	2^14 + 1.
32749	0x7FED	Largest 15 bit prime.
32767	0x7FFF	2^15 - 1. The maximum signed 16 bit value.
32768	0x8000	32k. 2^15. On a 16 bit platform, this value times 2 (the size of an integer) will overflow to 0.
32769	0x8001	2^15 + 1.
65280	0xFF00	Green in a 24 bit RGB format.
65521	0xFFE1	Largest 16 bit prime.
65535	0xFFFF	The maximum unsigned 16 bit value (2^16 - 1).

Raw List

256, 257, 260, 360, 365, 512, 1000, 1024, 1601, 1970, 1999, 2004, 2100, 3600, 4095, 4096, 4097, 9999, 16383, 16384, 16385, 32749, 32767, 32768, 32769, 65280, 65521, 65535

32 bit Integers (65,536 - 4,294,967,295)

Value	Hex	Description
65536	0x00010000	2^16.
65537	0x00010001	2^16 + 1.
131072	0x00020000	128k.
1048576	0x00100000	Megabyte.
5550100	0x0054B014	Start of the fictional phone number range.
5550199	0x0054B077	End of the fictional phone number range.
16711680	0x00FF0000	Red in a 32 bit RGB format.
16777215	0x00FFFFFF	White in a 24 bit RGB format.
999999999	0x3B9AC9FF	Nine nines. Largest 32 bit value with all 9s.
1073741824	0x40000000	Gigabyte. On a 32 bit platform, this value times 4 (the size of an integer) will overflow to 0.
1431655765	0x55555555	Repeating 01 bit pattern.
2130706433	0x7F000001	Equivalent to 127.0.0.1 in a packed IP format (loop back address).
2147483647	0x7FFFFFFF	The maximum signed 32 bit value. Largest 31 bit prime.
2851995649	0xA9FE0000	Equivalent to 169.254.0.1 in a packed IP format (auto IP address).
2863311530	0xAAAAAAAA	Repeating 10 bit pattern.
3221225472	0xC0000000	Three gigabytes, which is the size of addressable memory when Windows applications use the /LARGEADDRESSAWARE linker switch.
4294967291	0xFFFFFFFB	Largest 32 bit prime.
4294967295	0xFFFFFFFF	The maximum unsigned 32 bit value (2^32 - 1).

Raw List

65536, 65537, 131072, 1048576, 5550100, 5550199, 16711680, 16777215, 999999999, 1073741824, 1431655765, 2130706433, 2147483647, 2851995649, 2863311530, 3221225472, 4294967291, 4294967295

64 bit Integers (4,294,967,296 - 18,446,744,073,709,551,615)

Value	Hex	Description
4294967296	0x0000000100000000	2^32.
4294967297	0x0000000100000001	2^32 + 1.
36000000000	0x0000000861C46800	One hour in the Windows FILETIME format.
1099511627776	0x0000010000000000	Terabyte.
4222222222222	0x000003D7100E438E	Visa test credit card number.
30569309025904	0x00001BCD78CE3670	Diners Club test credit card number.
38520000023237	0x00002308A2EB0AC5	Diners Club test credit card number.
371449635398431	0x000151D4DB91E31F	American Express test credit card number.
378282246310005	0x0001580BB2EA8875	American Express test credit card number.
378734493671000	0x00015874FEF59E58	Corporate American Express test credit card number.
1125899906842624	0x0004000000000000	Petabyte.
3530111333300000	0x000C8A9E1809F720	JCB test credit card number.
3566002020360505	0x000CAB428BB12139	JCB test credit card number.
4012888888881881	0x000E41B380BEB2D9	Visa test credit card number.
4111111111111111	0x000E9B08A568F1C7	Visa test credit card number.
5105105105105100	0x00122310E854B0CC	MasterCard test credit card number.
5555555555554444	0x0013BCBF936B348C	MasterCard test credit card number.
5610591081018250	0x0013EECD885D338A	Australian BankCard test credit card number.
6011000990139424	0x0155AF93AC304200	Discover test credit card number.
6011111111111117	0x0155B12DE7BB1CD0	Discover test credit card number.
1152921504606846976	0x1000000000000000	Exabyte.
2305843009213693952	0x2000000000000000	On a 64 bit platform, this value times 8 (the size of an integer) will overflow to 0.
9223372036854775783	0x7FFFFFFFFFFFFFE7	Largest 63 bit prime.
9223372036854775807	0x7FFFFFFFFFFFFFFF	The maximum signed 64 bit value.
9999999999999999999	0x8AC7230489E7FFFF	Nineteen nines. Largest 64 bit value with all 9s.
18446744073709551557	0xFFFFFFFFFFFFFFC5	Largest 64 bit prime.
18446744073709551615	0xFFFFFFFFFFFFFFFF	The maximum unsigned 64 bit value.

Raw List

4294967296, 4294967297, 36000000000, 1099511627776, 4222222222222, 30569309025904, 38520000023237, 371449635398431, 378282246310005, 378734493671000, 1125899906842624, 3530111333300000, 3566002020360505, 4012888888881881, 4111111111111111, 5105105105105100, 5555555555554444, 5610591081018250, 6011000990139424, 6011111111111117, 1152921504606846976, 2305843009213693952, 9223372036854775783, 9223372036854775807, 9999999999999999999, 18446744073709551557, 18446744073709551615

Negative Integers

The constants here are the specific to signed integer values, and should be used when applications utilize negative inputs. To compliment your test cases, be sure to pull numbers from the above tables (after changing their sign) as many of them maintain appropriateness in the negative domain.

Value	Description
-1	Negative one.
-128	Minimum signed 8 bit value.
-32768	Minimum signed 16 bit value.
-2147483248	Minimum signed 32 bit value.
-9223372036854775808	Minimum signed 64 bit value.

Raw List

-1, -128, -32768, -2147483248, -9223372036854775808

Closing Thoughts

Since everything is stored as a number, this really only brushes the tip of what could (or should) be considered "important". For your own tests, you will want to think about the domain and come up with the best values to ensure good coverage in your code base. The numbers here are just stock values, and you will definitely want to "build your own" numbers. For example, look for hard coded values in the code you are testing, and use these. You will also want to look for interfaces which take a count of objects; fabricate and pass in a count which when multiplied by the size of the object will cause an integer overflow.

About the Author

Josh Poley has been a tester at Microsoft since 1998. He initially worked on the very first version of the Passport authentication service (currently called Windows Live ID). Then, in the spring of 2000, Josh moved over and joined a small handful of people who were starting to work on a project code-named Xbox. His initial responsibilities covered various pieces of the low level operating system (file systems, peripheral communication, etc.). Shortly after the Xbox game console launched in 2001, Josh took over as lead of the Kernel Test Team and remained in charge of validating the core operating system throughout the development and launch of the Xbox 360. Then, in the spring of 2007, Josh joined the Zune group as a Test Architect, where he helped solve various problems across the four main test teams in the organization. After a year in Zune, Josh went back to Xbox to help solve some more hard problems there.