Power of two

A power of two is a positive integer of the form 2n for positive n.

Because computers are based on binary, lots of things are limited at power of two based numbers (2n or 2n-1).

When a power of two minus one is prime, it is called a mersenne prime.

Examples
The first 20 powers of two are:

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576

Other powers of two are:

2^21 is equal to 2097152

2^22 is equal to 4194304

2^23 is equal to 8388608

2^24 is equal to 16777216

2^25 is equal to 33554432

2^26 is equal to 67108864

2^27 is equal to 134217728

2^28 is equal to 268435456

2^29 is equal to 536870912

2^30 is equal to 1073741824

2^31 is equal to 2147483648

2^32 is equal to 4294967296

2^33 is equal to 8589934592

2^34 is equal to 17179869184

2^35 is equal to 34359738368

2^36 is equal to 68719476736

2^37 is equal to 137438953472

2^38 is equal to 274877906944

2^39 is equal to 549755813888

2^40 is equal to 1099511627776

2^41 is equal to 2199023255552

2^42 is equal to 4398046511104

2^43 is equal to 8796093022208

2^44 is equal to 17592186044416

2^45 is equal to 35184372088832

2^46 is equal to 70368744177664

2^47 is equal to 140737488355328

2^48 is equal to 281474976710656

2^49 is equal to 562949953421312

2^50 is equal to 1.12589990684262E+15

2^51 is equal to 2.25179981368525E+15

2^52 is equal to 4.5035996273705E+15

2^53 is equal to 9.00719925474099E+15

2^54 is equal to 1.8014398509482E+16

2^55 is equal to 3.6028797018964E+16

2^56 is equal to 7.20575940379279E+16

2^57 is equal to 1.44115188075856E+17

2^58 is equal to 2.88230376151712E+17

2^59 is equal to 5.76460752303423E+17

2^60 is equal to 1.15292150460685E+18

2^61 is equal to 2.30584300921369E+18

2^62 is equal to 4.61168601842739E+18

2^63 is equal to 9.22337203685478E+18

2^64 is equal to 1.84467440737096E+19

2^65 is equal to 3.68934881474191E+19

2^66 is equal to 7.37869762948382E+19

2^67 is equal to 1.47573952589676E+20

2^68 is equal to 2.95147905179353E+20

2^69 is equal to 5.90295810358706E+20

2^70 is equal to 1.18059162071741E+21

2^71 is equal to 2.36118324143482E+21

2^72 is equal to 4.72236648286965E+21

2^73 is equal to 9.44473296573929E+21

2^74 is equal to 1.88894659314786E+22

2^75 is equal to 3.77789318629572E+22

2^76 is equal to 7.55578637259143E+22

2^77 is equal to 1.51115727451829E+23

2^78 is equal to 3.02231454903657E+23

2^79 is equal to 6.04462909807315E+23

2^80 is equal to 1.20892581961463E+24

2^81 is equal to 2.41785163922926E+24

2^82 is equal to 4.83570327845852E+24

2^83 is equal to 9.67140655691703E+24

2^84 is equal to 1.93428131138341E+25

2^85 is equal to 3.86856262276681E+25

2^86 is equal to 7.73712524553363E+25

2^87 is equal to 1.54742504910673E+26

2^88 is equal to 3.09485009821345E+26

2^89 is equal to 6.1897001964269E+26

2^90 is equal to 1.23794003928538E+27

2^91 is equal to 2.47588007857076E+27

2^92 is equal to 4.95176015714152E+27

2^93 is equal to 9.90352031428304E+27

2^94 is equal to 1.98070406285661E+28

2^95 is equal to 3.96140812571322E+28

2^96 is equal to 7.92281625142643E+28

2^97 is equal to 1.58456325028529E+29

2^98 is equal to 3.16912650057057E+29

2^99 is equal to 6.33825300114115E+29

2^100 is equal to 1.26765060022823E+30

2^1024 is equal to:

179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216

It is sometimes called "Infinity" because it is the max value for a floating-point number.