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¿Son reales las matemáticas?

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Los números primos más grandes del mundo y ¡el enigma de los números per...

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What is a function? Why 1+2+3+4+5+.... not equals -1/12 = Zeta(-1)

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Zeta Function - Part 14 - Riemann Xi Function

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Zeta Function - Part 13 - Trivial Zeros of the Zeta Function

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Zeta Function - Part 12 - Riemann Functional Equation II

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Zeta Function - Part 11 - Riemann Functional Equation I

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Zeta Function - Part 10 - Jacobi Theta Function

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Zeta Function - Part 9 - Relation to Gamma Function

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Zeta Function - Part 8 - Zeta of 2n - Part 3

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Zeta Function - Part 8 - Zeta of 2n - Part 2

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Zeta Function - Part 8 - Zeta of 2n - Part 1

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Zeta Function - Part 7 - Zeta of 2 aka The Basel Problem

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Zeta Function - Part 6 - The Prime Counting Function

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Zeta Function - Part 5 - Prime Zeta Function

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Zeta Function - Part 4 - Infinitude of Prime Numbers

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Zeta Function - Part 3 - Euler Product (easy)

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Zeta Function - Part 2 - Euler Product Representation

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Zeta Function - Part 1 - Convergence

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Divisibility Rule of Prime Numbers

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single primes

twin primes 18512parejas.pdf

single primes

run: 23 single prime. x-2=21. x+2=25. 37 single prime. x-2=35. x+2=39. 47 single prime. x-2=45. x+2=49. 53 single prime. x-2=51. x+2=55. 67 single prime. x-2=65. x+2=69. 79 single prime. x-2=77. x+2=81. 83 single prime. x-2=81. x+2=85. 89 single prime. x-2=87. x+2=91. 97 single prime. x-2=95. x+2=99. 113 single prime. x-2=111. x+2=115. 127 single prime. x-2=125. x+2=129. 131 single prime. x-2=129. x+2=133. 157 single prime. x-2=155. x+2=159. 163 single prime. x-2=161. x+2=165. 167 single prime. x-2=165. x+2=169. 173 single prime. x-2=171. x+2=175. 211 single prime. x-2=209. x+2=213. 223 single prime. x-2=221. x+2=225. 233 single prime. x-2=231. x+2=235. 251 single prime. x-2=249. x+2=253. 257 single prime. x-2=255. x+2=259. 263 single prime. x-2=261. x+2=265. 277 single prime. x-2=275. x+2=279. 293 single prime. x-2=291. x+2=295. 307 single prime. x-2=305. x+2=309. 317 single prime.

1000 parejas twin primes.

run: 1 5 7 twin primes 2 11 13 twin primes 3 17 19 twin primes 6 41 43 twin primes 8 59 61 twin primes 16 137 139 twin primes 17 149 151 twin primes 20 179 181 twin primes 21 191 193 twin primes 22 197 199 twin primes 24 227 229 twin primes 28 269 271 twin primes 34 347 349 twin primes 40 419 421 twin primes 41 431 433 twin primes 44 461 463 twin primes 54 599 601 twin primes 56 617 619 twin primes 61 677 679 twin primes 85 1019 1021 twin primes 86 1031 1033 twin primes 100 1229 1231 twin primes 104 1289 1291 twin primes 107 1319 1321 twin primes 112 1427 1429 twin primes 126 1607 1609 twin primes 132 1697 1699 twin primes 138 1787 1789 twin primes 153 2027 2029 twin primes 156 2081 2083 twin primes 157 2087 2089 twin primes 161 2141 2143 twin primes 171 2309 2311 twin primes 176 2381 2383 twin primes 186 2549 2551 twin primes 188 2591 2593 twin primes 197 2711 2713 twin prime

primesandfpp 2...

3645 potencia de dos menos 1

run: a= 3645,  n=5  M=116639 M is prime 5, a= 3645,  n=6  M=233279 M is prime 6, a= 3645,  n=9  M=1866239 M is prime 9, a= 3645,  n=10  M=3732479 M is prime 10, a= 3645,  n=11  M=7464959 M is prime 11, a= 3645,  n=12  M=14929919 M is prime 12, a= 3645,  n=13  M=29859839 M is prime 13, a= 3645,  n=17  M=477757439 M is prime 17, a= 3645,  n=20  M=3822059519 M is prime 20, a= 3645,  n=21  M=7644119039 M is prime 21, a= 3645,  n=23  M=30576476159 M is prime 23, a= 3645,  n=26  M=244611809279 M is prime 26, a= 3645,  n=29  M=1956894474239 M is prime 29, a= 3645,  n=43  M=32061759065948159 M is prime 43, a= 3645,  n=47  M=512988145055170559 M is prime 47, a= 3645,  n=52  M=16415620641765457919 M is prime 52, a= 3645,  n=54  M=65662482567061831679 M is prime 54, a= 3645,  n=64  M=67238382148671315640319 M is prime 64, a= 3645,  n=65  M=134476764297342631280639 M is prime 65, a= 3645,  n=67  M=537907057189370525122559 M is prime 67, a= 3645,  n=71  M=8606512915029928401960959 M is prime 71, a=

run: Por favor introduzca el número a evaluar: 37 El número a evaluar es:"37" Ahora es un BigInteger:37 número = 35. Primos generados FPP = 2498. número = 36. Primos generados FPP = 4542. número = 37. Primos generados FPP = 1495. número = 38. Primos generados FPP = 3020. número = 39. Primos generados FPP = 2260. ptp1=2498 b=4542 a=1495 c=3020 ptp2=2260 1552. b-(2a)>0, 30. c-(2a)>0, 1582. (bc)-4a>0. 37 es primo, cumple con los 3 criterios de primalidad BUILD SUCCESSFUL (total time: 8 seconds)

run: Por favor introduzca el número a evaluar: 37  El número a evaluar es:"37"  Ahora es un BigInteger:37 número = 35. Primos generados FPP =  2498. número = 36. Primos generados FPP =  4542. número = 37. Primos generados FPP =  1495. número = 38. Primos generados FPP =  3020. número = 39. Primos generados FPP =  2260.  ptp1=2498   b=4542   a=1495   c=3020   ptp2=2260  1552.   b-(2a)>0,   30.   c-(2a)>0,   1582.   (bc)-4a>0. 37 es primo, cumple con los 3 criterios de primalidad BUILD SUCCESSFUL (total time: 8 seconds)

run: Ahora es un BigInteger:10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087 número = 10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729085. Primos generados FPP = 21. número = 10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729086. Primos generados FPP = 84. número = 10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087. Primos generados FPP = 23. número = 10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729088. Primos generados FPP = 31. número = 10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729089. Primos generados FPP = 28. ptp1=21 b=84 a=23 c=31 ptp2=28 38. b-(2a)>0, -15. c-(2a)>0, 23. (bc)-4a>0. BUILD SUCCESSFUL (total time: 29 minutes 57 seconds)

run:  Ahora es un BigInteger:10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087 número = 10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729085. Primos generados FPP =  21. número = 104079321946643990819252403273640855386152622472667048053191123504036080596733602980122394417323241848424216139542810077913835662483234649081399066056

El número a evaluar es:"103333"

run: Por favor introduzca el número a evaluar: 103333  El número a evaluar es:"103333"  Ahora es un BigInteger:103333 número = 103331. Primos generados FPP =  9037. número = 103332. Primos generados FPP =  26297. número = 103333. Primos generados FPP =  8316. número = 103334. Primos generados FPP =  21308. número = 103335. Primos generados FPP =  15655.  ptp1=9037   b=26297   a=8316   c=21308   ptp2=15655  9665.   b-(2a)>0,   4676.   c-(2a)>0,   14341.   (bc)-4a>0. 103333 es primo, cumple con los 3 criterios de primalidad BUILD SUCCESSFUL (total time: 33 seconds)

run: Por favor introduzca el número a evaluar: 103 El número a evaluar es:"103" Ahora es un BigInteger:103 número = 101. Primos generados FPP = 116625. número = 102. Primos generados FPP = 338348. número = 103. Primos generados FPP = 104318. número = 104. Primos generados FPP = 219852. número = 105. Primos generados FPP = 218986. ptp1=116625 b=338348 a=104318 c=219852 ptp2=218986 129712. b-(2a)>0, 11216. c-(2a)>0, 140928. (bc)-4a>0. 103 es primo, cumple con los 3 criterios de primalidad BUILD SUCCESSFUL (total time: 1 minute 18 seconds)

run: Por favor introduzca el número a evaluar: 103  El número a evaluar es:"103"  Ahora es un BigInteger:103 número = 101. Primos generados FPP =  116625. número = 102. Primos generados FPP =  338348. número = 103. Primos generados FPP =  104318. número = 104. Primos generados FPP =  219852. número = 105. Primos generados FPP =  218986.  ptp1=116625   b=338348   a=104318   c=219852   ptp2=218986  129712.   b-(2a)>0,   11216.   c-(2a)>0,   140928.   (bc)-4a>0. 103 es primo, cumple con los 3 criterios de primalidad BUILD SUCCESSFUL (total time: 1 minute 18 seconds)

lista de primos

2   3   5   7   11   13   17   19   23   29   31   37   41   43   47   53   59   61   67   71  73  79  83  89  97  101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429