Interesting numbers

Here's some interesting numbers. They're not necessarily "interesting", but there's some useful qualities about them, especially for programmers.

Minimum divisible by all

These numbers are divisible by X and all whole numbers below it. For example the number 2520 is divisible by 10, 9, 8, 7, 6, 5, 4, 3, and 2.

Note: only the minimum values are listed, for example 24 is divisible by 4, 3, and 2, but it's redundant because 12 is divisible by the same numbers.

#	divisible by	Notes
2	<= 2
6	<= 3
12	<= 4
60	<= 6	fits into i8, u8
420	<= 7
840	<= 8
2520	<= 10
27,720	<= 12	fits into i16, u16
360,360	<= 15
720,720	<= 16
12,252,240	<= 18
232,792,560	<= 22	fits into i32, u32
5,354,228,880	<= 24
26,771,144,400	<= 26
80,313,433,200	<= 28
2,329,089,562,800	<= 30
72,201,776,446,800	<= 31
144,403,552,893,600	<= 36
5,342,931,457,063,200	<= 40
219,060,189,739,591,200	<= 42
9,419,588,158,802,421,600	<= 46	fits into i64, u64

Code used to generate this list

u64 latest = 2;
u64 maxcount = 0;
for (u64 i=2; i; i+=latest) {
	u64 count = 0;
	for (u64 x=2; !(i%x); x++) {
		count = x;
	}
	if (count > maxcount) {
		maxcount = count;
		latest = i;
		printf("%llu is divisible by <= %llu\n", i, count);
	}
	if (i < latest) break; // i overflowed
}

Power of 2

"Power of 2" basically means any number created with 2ˣ, also known as 2^x, also known as pow(2,x). Replace x with any number.

One use is that they represent the value range of a given number of bits. For example 4 bits (2^4) can represent 16 different values; 0 to 15.

#	Power	Notes
2	2^1
4	2^2
8	2^3
16	2^4
32	2^5
64	2^6
128	2^7	signed 8-bit integer range (-128 - 127)
256	2^8	unsigned 8-bit integer range (0 - 255)
512	2^9
1,024	2^10
2,048	2^11
4,096	2^12
8,192	2^13
16,384	2^14
32,768	2^15	signed 16-bit integer range (-32,768 - 32,767)
65,536	2^16	unsigned 16-bit integer range (0 - 65,535)
131,072	2^17
262,144	2^18
524,288	2^19
1,048,576	2^20
2,097,152	2^21
4,194,304	2^22
8,388,608	2^23
16,777,216	2^24	float can store integers roughly up to here
33,554,432	2^25
67,108,864	2^26
134,217,728	2^27
268,435,456	2^28
536,870,912	2^29
1,073,741,824	2^30
2,147,483,648	2^31	signed 32-bit integer range (-2,147,483,648 - 2,147,483,647)
4,294,967,296	2^32	unsigned 32-bit integer range (0 - 4,294,967,295)
8,589,934,592	2^33
7,179,869,184	2^34
4,359,738,368	2^35
8,719,476,736	2^36
137,438,953,472	2^37
274,877,906,944	2^38
549,755,813,888	2^39
1,099,511,627,776	2^40
2,199,023,255,552	2^41
4,398,046,511,104	2^42
8,796,093,022,208	2^43
17,592,186,044,416	2^44
35,184,372,088,832	2^45
70,368,744,177,664	2^46
140,737,488,355,328	2^47
281,474,976,710,656	2^48
562,949,953,421,312	2^49
1,125,899,906,842,624	2^50
2,251,799,813,685,248	2^51
4,503,599,627,370,496	2^52
9,007,199,254,740,992	2^53	double can store integers roughly up to here
18,014,398,509,481,984	2^54
36,028,797,018,963,968	2^55
72,057,594,037,927,936	2^56
144,115,188,075,855,872	2^57
288,230,376,151,711,744	2^58
576,460,752,303,423,488	2^59
1,152,921,504,606,846,976	2^60
2,305,843,009,213,693,952	2^61
4,611,686,018,427,387,904	2^62
9,223,372,036,854,775,808	2^63	signed 64-bit integer range (-9,223,372,036,854,775,808 - 9,223,372,036,854,775,807)
18,446,744,073,709,551,616	2^64	unsigned 64-bit integer range (0 - 18,446,744,073,709,551,615)
340,282,366,920,938,463,463,374,607,431,768,211,455	2^128	u128

Code used to generate this list

int power = 0;
u64 x = 1;
while (1) {
	power ++;
	x *= 2;
	printf("2^%i = %llu\n", power, x);
	if (x == 0) break; // x overflowed
}
printf("2^64 = %llu + 1\n", (u64)(U64_MAX));