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127 (number)

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From Wikipedia, the free encyclopedia

Natural number

← 126

127

128 →

←120 121 122 123 124 125 126 127 128 129 →

←0 100 200 300 400 500 600 700 800 900 →

Cardinal

one hundred twenty-seven

Ordinal

127th
(one hundred twenty-seventh)

31st

1, 127

ΡΚΖ´

CXXVII,cxxvii

1111111₂

11201₃

331₆

177₈

A7₁₂

7F₁₆

127 (one hundred [and] twenty-seven) is thenatural number following126 and preceding128. It is also a prime number.

In mathematics

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As aMersenne prime, 127 is related to theperfect number8128. 127 is also thelargest known Mersenne prime exponent for a Mersenne number, $2^{127}-1$ , which is also a Mersenne prime. It was discovered byÉdouard Lucas in 1876 and held the record for thelargest known prime for 75 years.
- $2^{127}-1$ is the largest prime ever discovered by hand calculations as well as the largest knowndouble Mersenne prime.
- Furthermore, 127 is equal to $2^{7}-1$ , and 7 is equal to $2^{3}-1$ , and 3 is the smallest Mersenne prime, making 7 the smallest double Mersenne prime and 127 the smallest triple Mersenne prime.
There are a total of 127prime numbers between2,000 and3,000.
127 is also acuban prime of the form $p={\frac {x^{3}-y^{3}}{x-y}}$ , $x=y+1$ .^[1] The next prime is 131, with which it comprises acousin prime. Because the nextodd number, 129, is asemiprime, 127 is aChen prime.^[2] 127 is greater than the arithmetic mean of its two neighboring primes; thus, it is astrong prime.^[3]
127 is acentered hexagonal number.^[4]
It is the seventhMotzkin number.^[5]
127 is apalindromic prime innonary andbinary.
127 is the firstFriedman prime in decimal. It is also the first nice Friedman number in decimal, since $127=2^{7}-1\,$ , as well as binary since $1111111=(1+1)^{111}-1\,$ .
127 is the sum of the sums of the divisors of the first twelvepositive integers.^[6]
127 is the smallest prime that can be written as the sum of the first two or more odd primes: $127=3+5+7+11+13+17+19+23+29$ .^[7]
127 is the smallest odd number that cannot be written in the form $p+2^{x}$ , forp is aprime number, andx is aninteger, since $127-2^{0}=126,$ $127-2^{1}=125,$ $127-2^{2}=123,$ $127-2^{3}=119,$ $127-2^{4}=111,$ $127-2^{5}=95,$ and $127-2^{6}=63$ are allcomposite numbers.^[8]
127 is an isolated prime where neither $p-2$ nor $p+2$ is prime.
127 is the smallest digitally delicate prime in binary.^[9]
127 is the 31st prime number and therefore it is the smallestMersenne prime with a Mersenne prime index.
127 is the largest number with the property $127=1\cdot {\textrm {prime}}(1)+2\cdot {\textrm {prime}}(2)+7\cdot {\textrm {prime}}(7),$ where ${\textrm {prime}}(n)$ is thenth prime number. There are only two numbers with that property; the other one is43.
127 is equal to ${\textrm {prime}}^{6}(1),$ where ${\textrm {prime}}(n)$ is thenth prime number.
127 is the number of non-equivalent ways of expressing 10,000 as the sum of two prime numbers.^[10]
127 is the integer as floor of the imaginary part of the 42th non-trivial zero of the Riemann zeta-function.^[11]
127 is the smallest prime number that results in a decimal greater than 4 when divided by its prime index. 127 divided by 31 is 4 with a remainder of 3.
127 is aLucky number which is generated by a certain "sieve".^[12]
127 is the 8th term in the prime number variation of Flavius's sieve.^[13]
127 is aFortunate number which is linked to the primorials.^[14]

In other fields

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The non-printable "Delete" (DEL) control character inASCII.
Linotype (and Intertype) machines used brass matrices with one of 127 possible combinations punched into the top to enable the matrices to return to their proper channel in the magazine.

References

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^"Sloane's A002407 : Cuban primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^Sloane, N. J. A. (ed.)."Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^"Sloane's A051634 : Strong primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Sloane's A003215 : Hex (or centered hexagonal) numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Sloane's A001006 : Motzkin numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^Sloane, N. J. A. (ed.)."Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A071148".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Partial sums of a sequence of odd primes; a(n) = sum of the first n odd primes.
^Sloane, N. J. A. (ed.)."Sequence A006285 (Odd numbers not of form p + 2^x (de Polignac numbers))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A137985".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Complementing any single bit in the binary representation of these primes produces a composite number.
^Sloane, N. J. A. (ed.)."Sequence A065577 (Number of Goldbach partitions of 10^n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-08-31.
^Sloane, N. J. A. (ed.)."Sequence A013629".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Floor of imaginary parts of nontrivial zeros of Riemann zeta function.
^Sloane, N. J. A. (ed.)."Sequence A000959".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Lucky numbers
^Sloane, N. J. A. (ed.)."Sequence A099243".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.. A variation on Flavius's sieve.
^Sloane, N. J. A. (ed.)."Sequence A005235".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.. Fortunate numbers: least m > 1 such that m + prime(n)# is prime, where p# denotes the product of all primes <= p.

Wells, D.The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 136 - 138

v
t
e

\mathbb {Z}

Integers

−2,−1

0 to 199

0 to 99	100 to 199
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99	100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

200 to 399

200 to 299	300 to 399
200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299	300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 318 323 325 341 353 359 360 363 365 369 377 384

400 to 999

400s, 500s, and 600s	700s, 800s, and 900s
400 420 440 495 496 500 501 511 512 555 600 610 613 616 666 693	700 720 743 744 777 786 800 801 836 840 880 881 888 900 911 971 987 999

1000s and 10,000s
1000s	1000 1001 1023 1024 1089 1093 1105 1234 1289 1458 1510 1728 1729 1980 1987 2000 2520 3000 3511 4000 5000 5040 6000 6174 7000 7744 7825 8000 8128 8192 9000 9855 9999
10,000s	10,000 16,807 20,000 30,000 40,000 50,000 60,000 64,079 65,535 65,536 65,537 70,000 80,000 90,000

100,000s to 10,000,000,000,000s
100,000 142,857 144,000 1,000,000 10,000,000 43,112,609 100,000,000 1,000,000,000 2,147,483,647 4,294,967,295 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000

Large numbers

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