2 To The 9th Power

2 raised to an integer power

Visualization of powers of two from 1 to 1024 (2⁰ to ii¹⁰)

A power of two is a number of the grade $ii n$ where $northward$ is an integer, that is, the result of exponentiation with number two as the base and integer $n$ as the exponent.

In a context where only integers are considered, $northward$ is restricted to non-negative values,^[ane] so there are 1, 2, and 2 multiplied by itself a certain number of times.^[2]

The first ten powers of 2 for not-negative values of $due north$ are:

i, two, 4, 8, sixteen, 32, 64, 128, 256, 512, ... (sequence A000079 in the OEIS)

Considering two is the base of the binary numeral organization, powers of 2 are common in computer science. Written in binary, a ability of two always has the course 100...000 or 0.00...001, just similar a ability of x in the decimal organization.

Computer science [edit]

Two to the exponent of $n$ , written as $2 n$ , is the number of ways the bits in a binary word of length $n$ can exist arranged. A word, interpreted as an unsigned integer, tin represent values from 0 ( $000...000 2$ ) to $two n - 1$ ( $111...111 2$ ) inclusively. Corresponding signed integer values can be positive, negative and zero; see signed number representations. Either mode, one less than a ability of two is often the upper leap of an integer in binary computers. As a outcome, numbers of this form show upward oft in computer software. As an instance, a video game running on an 8-bit organization might limit the score or the number of items the role player can agree to 255—the issue of using a byte, which is 8 bits long, to store the number, giving a maximum value of $28 - 1 = 255$ . For example, in the original Legend of Zelda the main graphic symbol was express to carrying 255 rupees (the currency of the game) at any given fourth dimension, and the video game Pac-Man famously has a kill screen at level 256.

Powers of two are often used to measure calculator retentiveness. A byte is now considered eight bits (an octet), resulting in the possibility of 256 values (2⁸). (The term byte once meant (and in some cases, still means) a collection of bits, typically of five to 32 bits, rather than only an eight-scrap unit.) The prefix kilo, in conjunction with byte, may exist, and has traditionally been, used, to mean one,024 (2^ten). However, in full general, the term kilo has been used in the International System of Units to mean ane,000 (10³). Binary prefixes have been standardized, such as kibi (Ki) meaning 1,024. Nearly all processor registers accept sizes that are powers of two, 32 or 64 being very common.

Powers of 2 occur in a range of other places as well. For many deejay drives, at to the lowest degree one of the sector size, number of sectors per track, and number of tracks per surface is a power of 2. The logical cake size is nearly ever a power of two.

Numbers that are non powers of ii occur in a number of situations, such as video resolutions, but they are ofttimes the sum or production of only two or three powers of 2, or powers of two minus 1. For instance, $640 = 32 \times twenty$ , and $480 = 32 \times 15$ . Put some other fashion, they accept fairly regular bit patterns.

Mersenne and Fermat primes [edit]

A prime number that is one less than a power of two is called a Mersenne prime number. For example, the prime number number 31 is a Mersenne prime because it is 1 less than 32 (2⁵). Similarly, a prime number (like 257) that is one more than than a positive power of two is called a Fermat prime—the exponent itself is a power of two. A fraction that has a power of two as its denominator is called a dyadic rational. The numbers that tin exist represented equally sums of sequent positive integers are called polite numbers; they are exactly the numbers that are not powers of 2.

Euclid'southward Elements, Volume 9 [edit]

The geometric progression 1, two, four, 8, 16, 32, ... (or, in the binary numeral system, 1, 10, 100, thou, 10000, 100000, ... ) is important in number theory. Book Nine, Proposition 36 of Elements proves that if the sum of the first $north$ terms of this progression is a prime number (and thus is a Mersenne prime number as mentioned above), and then this sum times the $n$ th term is a perfect number. For example, the sum of the first 5 terms of the serial 1 + 2 + iv + viii + xvi = 31, which is a prime number. The sum 31 multiplied by 16 (the 5th term in the series) equals 496, which is a perfect number.

Volume Ix, Proposition 35, proves that in a geometric series if the showtime term is subtracted from the second and concluding term in the sequence, then as the backlog of the second is to the first—then is the excess of the last to all those earlier it. (This is a restatement of our formula for geometric series from higher up.) Applying this to the geometric progression 31, 62, 124, 248, 496 (which results from ane, ii, iv, eight, 16 by multiplying all terms by 31), we see that 62 minus 31 is to 31 every bit 496 minus 31 is to the sum of 31, 62, 124, 248. Therefore, the numbers 1, ii, 4, viii, sixteen, 31, 62, 124 and 248 add together upwards to 496 and farther these are all the numbers that split 496. For suppose that $p$ divides 496 and it is not amongst these numbers. Presume $p q$ is equal to $xvi \times 31$ , or 31 is to $q$ as $p$ is to xvi. Now $p$ cannot divide xvi or information technology would be among the numbers 1, two, 4, 8 or xvi. Therefore, 31 cannot dissever $q$ . And since 31 does non dissever $q$ and $q$ measures 496, the fundamental theorem of arithmetic implies that $q$ must divide xvi and exist amongst the numbers 1, 2, 4, eight or 16. Let $q$ exist 4, then $p$ must exist 124, which is incommunicable since by hypothesis $p$ is not amongst the numbers 1, two, four, eight, xvi, 31, 62, 124 or 248.

Table of values [edit]

(sequence A000079 in the OEIS)


$north$	$2 n$	$due north$	$2 n$	$due north$	$2 north$	$north$	$2 n$
0	1	16	65,536	32	four,294,967,296	48	281,474,976,710,656
1	2	17	131,072	33	eight,589,934,592	49	562,949,953,421,312
two	4	18	262,144	34	17,179,869,184	fifty	1,125,899,906,842,624
3	8	19	524,288	35	34,359,738,368	51	ii,251,799,813,685,248
4	16	xx	one,048,576	36	68,719,476,736	52	4,503,599,627,370,496
5	32	21	2,097,152	37	137,438,953,472	53	9,007,199,254,740,992
6	64	22	4,194,304	38	274,877,906,944	54	18,014,398,509,481,984
seven	128	23	8,388,608	39	549,755,813,888	55	36,028,797,018,963,968
8	256	24	16,777,216	40	1,099,511,627,776	56	72,057,594,037,927,936
ix	512	25	33,554,432	41	2,199,023,255,552	57	144,115,188,075,855,872
ten	1,024	26	67,108,864	42	4,398,046,511,104	58	288,230,376,151,711,744
11	ii,048	27	134,217,728	43	8,796,093,022,208	59	576,460,752,303,423,488
12	iv,096	28	268,435,456	44	17,592,186,044,416	threescore	1,152,921,504,606,846,976
13	8,192	29	536,870,912	45	35,184,372,088,832	61	two,305,843,009,213,693,952
14	xvi,384	30	1,073,741,824	46	70,368,744,177,664	62	iv,611,686,018,427,387,904
xv	32,768	31	2,147,483,648	47	140,737,488,355,328	63	9,223,372,036,854,775,808

Starting with two the last digit is periodic with period iv, with the bicycle 2–four–8–half dozen–, and starting with 4 the last 2 digits are periodic with period 20. These patterns are generally true of whatsoever power, with respect to whatsoever base of operations. The pattern continues where each blueprint has starting point $ii thou$ , and the catamenia is the multiplicative order of 2 modulo $five k$ , which is $φ (5 grand) = iv \times 5 one thousand -1$ (run across Multiplicative group of integers modulo n).^{[ commendation needed ]}

Powers of 1024 [edit]

(sequence A140300 in the OEIS)

The commencement few powers of 2¹⁰ are slightly larger than those aforementioned powers of 1000 (10³):

2⁰	=	ane	= g⁰	(0% deviation)
2¹⁰	=	ane 024	≈ 1000¹	(ii.iv% deviation)
2^xx	=	1 048 576	≈ 1000^two	(4.ix% deviation)
two³⁰	=	one 073 741 824	≈ grand³	(7.iv% deviation)
2^xl	=	1 099 511 627 776	≈ 1000⁴	(ten.0% deviation)
2⁵⁰	=	1 125 899 906 842 624	≈ 1000⁵	(12.vi% deviation)
2^threescore	=	i 152 921 504 606 846 976	≈ 1000⁶	(15.3% deviation)
ii⁷⁰	=	1 180 591 620 717 411 303 424	≈ 1000⁷	(18.i% deviation)
ii⁸⁰	=	1 208 925 819 614 629 174 706 176	≈ one thousand⁸	(20.ix% deviation)
2⁹⁰	=	1 237 940 039 285 380 274 899 124 224	≈ k^nine	(23.8% divergence)
2¹⁰⁰	=	1 267 650 600 228 229 401 496 703 205 376	≈ 1000¹⁰	(26.8% difference)
2¹¹⁰	=	1 298 074 214 633 706 907 132 624 082 305 024	≈ 1000¹¹	(29.8% deviation)
ii¹²⁰	=	one 329 227 995 784 915 872 903 807 060 280 344 576	≈ one thousand¹²	(32.9% deviation)
2¹³⁰	=	i 361 129 467 683 753 853 853 498 429 727 072 845 824	≈ one thousand^thirteen	(36.1% deviation)
2¹⁴⁰	=	1 393 796 574 908 163 946 345 982 392 040 522 594 123 776	≈ 1000¹⁴	(39.4% deviation)
2¹⁵⁰	=	i 427 247 692 705 959 881 058 285 969 449 495 136 382 746 624	≈ yard¹⁵	(42.7% deviation)

Powers of two whose exponents are powers of two [edit]

Because information (specifically integers) and the addresses of information are stored using the same hardware, and the data is stored in one or more octets ( $23$ ), double exponentials of two are mutual. For example,

$due north$	$ii n$	$2 ii n$ (sequence A001146 in the OEIS)
0	1	2
1	2	iv
2	four	16
iii	8	256
4	16	65,536
five	32	4,294,967,296
six	64	18,446,744,073,709,551,616 (20 digits)
vii	128	340,282,366,920,938,463,463,374,607,431,768,211,456 (39 digits)
8	256	115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 (78 digits)
ix	512	thirteen,407,807,929,942,597,099,574,024,998,205,846,127,479,365,820,592,393,377,723,561,443,721,764,030,073,546,976,801,874,298,166,903,427,690,031,858,186,486,050,853,753,882,811,946,569,946,433,649,006,084,096 (155 digits)
x	i,024	179,769,313,486,231,590,772,930,...,304,835,356,329,624,224,137,216 (309 digits)
eleven	ii,048	32,317,006,071,311,007,300,714,8...,193,555,853,611,059,596,230,656 (617 digits)
12	4,096	1,044,388,881,413,152,506,691,75...,243,804,708,340,403,154,190,336 (ane,234 digits)
13	viii,192	ane,090,748,135,619,415,929,462,98...,997,186,505,665,475,715,792,896 (2,467 digits)
fourteen	sixteen,384	1,189,731,495,357,231,765,085,75...,460,447,027,290,669,964,066,816 (4,933 digits)
fifteen	32,768	1,415,461,031,044,954,789,001,55...,541,122,668,104,633,712,377,856 (nine,865 digits)
xvi	65,536	2,003,529,930,406,846,464,979,07...,339,445,587,895,905,719,156,736 (19,729 digits)
17	131,072	4,014,132,182,036,063,039,166,06...,850,665,812,318,570,934,173,696 (39,457 digits)
xviii	262,144	16,113,257,174,857,604,736,195,7...,753,862,605,349,934,298,300,416 (78,914 digits)

Several of these numbers stand for the number of values representable using common computer data types. For example, a 32-bit discussion consisting of iv bytes can represent $232$ singled-out values, which can either exist regarded as mere bit-patterns, or are more than commonly interpreted as the unsigned numbers from 0 to $232 - 1$ , or equally the range of signed numbers between $-2 31$ and $ii 31 - 1$ . As well see tetration and lower hyperoperations. For more than about representing signed numbers encounter ii's complement.

In a connection with nimbers, these numbers are often called Fermat 2-powers.

The numbers $2^{two^{n}}$ course an irrationality sequence: for every sequence $x_{i}$ of positive integers, the series

\sum _{i=0}^{\infty }{\frac {one}{2^{two^{i}}x_{i}}}={\frac {i}{2x_{0}}}+{\frac {1}{4x_{ane}}}+{\frac {1}{16x_{2}}}+\cdots

converges to an irrational number. Despite the rapid growth of this sequence, it is the slowest-growing irrationality sequence known.^[iii]

Selected powers of two [edit]

2⁸ = 256: The number of values represented by the 8 $.25 in a byte, more specifically termed as an octet. (The term byte is often divers every bit a collection of bits rather than the strict definition of an 8-bit quantity, equally demonstrated by the term kilobyte.)
two¹⁰ = one,024: The binary approximation of the kilo-, or 1,000 multiplier, which causes a change of prefix. For example: 1,024 bytes = 1 kilobyte (or kibibyte).
2¹² = four,096: The hardware page size of an Intel x86-uniform processor.
two^fifteen = 32,768: The number of non-negative values for a signed 16-bit integer.
ii^xvi = 65,536: The number of distinct values representable in a single word on a 16-fleck processor, such as the original x86 processors.^[4]; The maximum range of a short integer variable in the C#, and Java programming languages. The maximum range of a Word or Smallint variable in the Pascal programming linguistic communication.; The number of binary relations on a iv-chemical element set.
ii²⁰ = 1,048,576: The binary approximation of the mega-, or ane,000,000 multiplier, which causes a change of prefix. For instance: 1,048,576 bytes = 1 megabyte (or mebibyte).
2²⁴ = xvi,777,216: The number of unique colors that can be displayed in truecolor, which is used by mutual calculator monitors.; This number is the upshot of using the three-aqueduct RGB system, with 8 bits for each aqueduct, or 24 $.25 in total.; The size of the largest unsigned integer or address in computers with 24-bit registers or information buses.
two²⁹ = 536,870,912: The largest power of ii with distinct digits in base of operations ten.^[5]
2^thirty = one,073,741,824: The binary approximation of the giga-, or i,000,000,000 multiplier, which causes a change of prefix. For example, 1,073,741,824 bytes = 1 gigabyte (or gibibyte).
2³¹ = 2,147,483,648: The number of non-negative values for a signed 32-bit integer. Since Unix time is measured in seconds since January ane, 1970, information technology volition run out at 2,147,483,647 seconds or 03:xiv:07 UTC on Tuesday, 19 January 2038 on 32-bit computers running Unix, a problem known as the year 2038 problem.
ii³² = 4,294,967,296: The number of distinct values representable in a single word on a 32-bit processor.^[6] Or, the number of values representable in a doubleword on a 16-chip processor, such as the original x86 processors.^[4]; The range of an int variable in the Java and C# programming languages.; The range of a Cardinal or Integer variable in the Pascal programming language.; The minimum range of a long integer variable in the C and C++ programming languages.; The total number of IP addresses under IPv4. Although this is a seemingly large number, nosotros've already run out of numbers for IPv4 addresses (but not for (IPv6]] addresses). See: IPv4 address exhaustion.; The number of binary operations with domain equal to whatsoever 4-element gear up, such every bit GF(4).
ii^forty = 1,099,511,627,776: The binary approximation of the tera-, or 1,000,000,000,000 multiplier, which causes a change of prefix. For example, 1,099,511,627,776 bytes = i terabyte or tebibyte.
2⁵⁰ = 1,125,899,906,842,624: The binary approximation of the peta-, or 1,000,000,000,000,000 multiplier. ane,125,899,906,842,624 bytes = 1 petabyte or pebibyte.
ii⁵³ = 9,007,199,254,740,992: The number until which all integer values tin exactly be represented in IEEE double precision floating-point format. Also the starting time power of 2 to start with the digit 9 in decimal.
2⁵⁶ = 72,057,594,037,927,936: The number of dissimilar possible keys in the obsolete 56 bit DES symmetric nil.
2⁶⁰ = 1,152,921,504,606,846,976: The binary approximation of the exa-, or 1,000,000,000,000,000,000 multiplier. 1,152,921,504,606,846,976 bytes = 1 exabyte or exbibyte.
2⁶³ = 9,223,372,036,854,775,808: The number of non-negative values for a signed 64-scrap integer.; two⁶³ − i, a common maximum value (equivalently the number of positive values) for a signed 64-bit integer in programming languages.
two⁶⁴ = 18,446,744,073,709,551,616: The number of distinct values representable in a single give-and-take on a 64-scrap processor. Or, the number of values representable in a doubleword on a 32-bit processor. Or, the number of values representable in a quadword on a 16-bit processor, such equally the original x86 processors.^[4]; The range of a long variable in the Java and C# programming languages.; The range of a Int64 or QWord variable in the Pascal programming language.; The total number of IPv6 addresses generally given to a single LAN or subnet.; 2⁶⁴ − 1, the number of grains of rice on a chessboard, according to the old story, where the first square contains one grain of rice and each succeeding square twice as many as the previous foursquare. For this reason the number is sometimes known equally the "chess number".; 2⁶⁴ − 1 is as well the number of moves required to complete the legendary 64-disk version of the Tower of Hanoi.
2⁶⁸ = 295,147,905,179,352,825,856: The first power of 2 to comprise all decimal digits. (sequence A137214 in the OEIS)
2⁷⁰ = 1,180,591,620,717,411,303,424: The binary approximation of the zetta-, or one,000,000,000,000,000,000,000 multiplier. one,180,591,620,717,411,303,424 bytes = 1 zettabyte (or zebibyte).
2⁸⁰ = one,208,925,819,614,629,174,706,176: The binary approximation of the yotta-, or ane,000,000,000,000,000,000,000,000 multiplier. 1,208,925,819,614,629,174,706,176 bytes = 1 yottabyte (or yobibyte).
2⁸⁶ = 77,371,252,455,336,267,181,195,264: ii⁸⁶ is conjectured to be the largest ability of ii non containing a zero in decimal.^[vii]
2⁹⁶ = 79,228,162,514,264,337,593,543,950,336: The total number of IPv6 addresses more often than not given to a local Internet registry. In CIDR notation, ISPs are given a / 32 , which means that 128-32=96 bits are available for addresses (as opposed to network designation). Thus, 2⁹⁶ addresses.
2¹⁰⁸ = 324,518,553,658,426,726,783,156,020,576,256: The largest known power of 2 not containing a ix in decimal. (sequence A035064 in the OEIS)
ii¹²⁶ = 85,070,591,730,234,615,865,843,651,857,942,052,864: The largest known power of two non containing a pair of sequent equal digits. (sequence A050723 in the OEIS)
2¹²⁸ = 340,282,366,920,938,463,463,374,607,431,768,211,456: The total number of IP addresses available under IPv6. Also the number of distinct universally unique identifiers (UUIDs).
two¹⁶⁸ = 374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856: The largest known power of 2 not containing all decimal digits (the digit 2 is missing in this case). (sequence A137214 in the OEIS)
two¹⁹² = 6,277,101,735,386,680,763,835,789,423,207,666,416,102,355,444,464,034,512,896: The total number of different possible keys in the AES 192-chip key space (symmetric zip).
ii²²⁹ = 862,718,293,348,820,473,429,344,482,784,628,181,556,388,621,521,298,319,395,315,527,974,912: ii²²⁹ is the largest known power of two containing the least number of zeros relative to its ability. It is conjectured by Metin Sariyar that every digit 0 to 9 is inclined to appear an equal number of times in the decimal expansion of power of ii as the power increases. (sequence A330024 in the OEIS)
2²⁵⁶ = 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936: The full number of different possible keys in the AES 256-flake primal space (symmetric cipher).
ii³³³ = 17,498,005,798,264,095,394,980,017,816,940,970,922,825,355,447,145,699,491,406,164,851,279,623,993,595,007,385,788,105,416,184,430,592: The smallest power of 2 greater than a googol (x¹⁰⁰).
2¹⁰²⁴ = 179,769,313,486,231,590,772,931,...,304,835,356,329,624,224,137,216: The maximum number that can fit in an IEEE double-precision floating-point format, and hence the maximum number that can be represented by many programs, for case Microsoft Excel.
ii^82,589,933 = 148,894,445,742,041,...,210,325,217,902,592: I more than the largest known prime number equally of Dec 2018^[update]. It has 24,862,047 digits.^[8]

Other properties [edit]

As each increase in dimension doubles the number of shapes, the sum of coefficients on each row of Pascal's triangle is a power of two

The sum of powers of ii from naught to a given power, inclusive, is i less than the side by side power of two, whereas the sum of powers of two from minus-infinity to a given ability, inclusive, equals the next power of two

The sum of all $n$ -cull binomial coefficients is equal to $2 n$ . Consider the set of all $northward$ -digit binary integers. Its cardinality is $two northward$ . Information technology is as well the sums of the cardinalities of certain subsets: the subset of integers with no 1s (consisting of a single number, written as $n$ 0s), the subset with a single 1, the subset with ii 1s, and so on up to the subset with $n$ 1s (consisting of the number written every bit $n$ 1s). Each of these is in plow equal to the binomial coefficient indexed by $northward$ and the number of 1s existence considered (for case, at that place are 10-choose-iii binary numbers with x digits that include exactly three 1s).

Currently, powers of two are the just known near perfect numbers.

The number of vertices of an $northward$ -dimensional hypercube is $2 due north$ . Similarly, the number of $(n - 1)$ -faces of an $n$ -dimensional cross-polytope is also $2 n$ and the formula for the number of $x$ -faces an $north$ -dimensional cross-polytope has is $ii^{x}{\tbinom {n}{x}}.$

The sum of the reciprocals of the powers of 2 is ane. The sum of the reciprocals of the squared powers of two (powers of four) is 1/3.

The smallest natural power of two whose decimal representation begins with seven is^[nine]

2^{46}=70\ 368\ 744\ 177\ 664.

Every power of 2 (excluding i) can be written as the sum of iv square numbers in 24 means. The powers of two are the natural numbers greater than i that can exist written as the sum of four square numbers in the fewest ways.

Equally a existent polynomial, a ^northward + b ⁿ is irreducible, if and only if n is a power of two. (If northward is odd, then a ⁿ + b ⁿ is divisible by a+n, and if n is fifty-fifty but not a power of ii, and then n can be written as due north=mp, where thou is odd, and thus $a^{n}+b^{n}=(a^{p})^{yard}+(b^{p})^{m}$ , which is divisible by a ^p + b ^p.) Merely in the domain of circuitous numbers, the polynomial $a^{2n}+b^{2n}$ (where northward>=one) can ever be factorized as $a^{2n}+b^{2n}=(a^{n}+b^{n}i)\cdot (a^{n}-b^{due north}i)$ , fifty-fifty if n is a power of ii.

Powers of two in music theory [edit]

In musical note, all unmodified note values take a elapsing equal to a whole note divided past a power of two; for case a half notation (1/2), a quarter note (1/iv), an eighth note (1/8) and a sixteenth note (i/16). Dotted or otherwise modified notes have other durations. In time signatures the lower numeral, the trounce unit of measurement, which tin be seen as the denominator of a fraction, is almost always a power of ii.

If the ratio of frequencies of two pitches is a ability of 2, so the interval between those pitches is full octaves. In this case, the corresponding notes have the same name.

Run into also [edit]

2048 (video game)
Binary number
Fermi–Dirac prime number
Geometric progression
Gould's sequence
Inchworm Vocal
Integer binary logarithm
Octave (electronics)
Power of 10
Power of three
Sum-gratuitous sequence

References [edit]

^ Lipschutz, Seymour (1982). Schaum's Outline of Theory and Problems of Essential Calculator Mathematics. New York: McGraw-Colina. p. 3. ISBN0-07-037990-4.
^ Sewell, Michael J. (1997). Mathematics Masterclasses. Oxford: Oxford University Press. p. 78. ISBN0-19-851494-8.
^ Guy, Richard G. (2004), "E24 Irrationality sequences", Unsolved bug in number theory (3rd ed.), Springer-Verlag, p. 346, ISBN0-387-20860-7, Zbl 1058.11001, archived from the original on 2016-04-28
^ ^a ^b ^c Though they vary in discussion size, all x86 processors use the term "word" to mean 16 bits; thus, a 32-bit x86 processor refers to its native wordsize every bit a dword
^ Prime Curios!: 536870912 "Prime Curios! 536870912". Archived from the original on 2017-09-05. Retrieved 2017-09-05 .
^ "Powers of two Table - - - - - - Vaughn's Summaries". www.vaughns-1-pagers.com. Archived from the original on Baronial 12, 2015.
^ Weisstein, Eric Due west. "Zero." From MathWorld--A Wolfram Spider web Resource. "Zero". Archived from the original on 2013-06-01. Retrieved 2013-05-29 .
^ "Mersenne Prime Discovery - two^82589933-i is Prime!". world wide web.mersenne.org.
^ Paweł Strzelecki (1994). "O potęgach dwójki (Near powers of two)" (in Polish). Delta. Archived from the original on 2016-05-09.

2 To The 9th Power,

Source: https://en.wikipedia.org/wiki/Power_of_two

Posted by: heiserluelf1998.blogspot.com

2 To The 9th Power

Computer science [edit]

Mersenne and Fermat primes [edit]

Euclid'southward Elements, Volume 9 [edit]

Table of values [edit]

Powers of 1024 [edit]

Powers of two whose exponents are powers of two [edit]

Selected powers of two [edit]

Other properties [edit]

Powers of two in music theory [edit]

Run into also [edit]

References [edit]

2 To The 9th Power,

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