Hipòtesi Àvalon. Annex III (b)

Taula de Primers més enllà de 10²²

201467286689315906290 = # {Primers ≤ x = 10²²} = 1 REAL

 

4.- Tram 21, P₂₁. 10²⁵_10²⁶.

Càlculs

x₂₀ 1,0423750077, P_n+1 = P_n^x. P₂₁ = P₂₀^x20 = 1524682550204370218534749

β₂₀ 0,8169914692, P_n+1 = e^{e^(βn) + LnPn}. P₂₁ = 1524682539930379961838030

A₂₀ 3,3060542417, P_{n+1 = e}^{LnPn (An  +  LnPn) / LnPn + 1}. P₂₁ = 1524682539889696848753019

[α₂₀ 0,9573277945], ᴫ = A₂₀^α20 = 3,1415926537052375616842237410935

k₂₀ 8,2735588959, P_n+1 = (P₁^1/n + P₁^1/n k_n)ⁿ. P₂₁ = 1524682539822176238878485

ζ₂₀ 8,6184125364, P_n+1 = (P_n + P_n ζ_n). P₂₁ = 1524682539883258379921250

∆₂₀ 0,0389058589, P_n+1 = e^{ln10 Pn – ∆n}. P₂₁ = 1524682541031877393473586

σ₂₀ 59,0286814769, P_n+1 = 9·10ⁿ⁺⁵/σ_n. P₂₁ = 1524682539880552247660160

Ordenats de majors a menors

1524682550204370218534749, x₂₀

1524682541031877393473586, ∆₂₀

1524682539930379961838030, β₂₀

1524682539889696848753019, A₂₀

1524682539883258379921250, ζ₂₀

1524682539880552247660160, σ₂₀

1524682539822176238878485, k₂₀

 

5.- Tram 22, P₂₂. 10²⁶_10²⁷.

Càlculs

x₂₁ 1,0406898729, P_n+1 = P_n^x. P₂₂ = P₂₁^x21 = 14695688141774904562112384

β₂₁ 0,8179137312, P_n+1 = e^{e^(βn) + LnPn}. P₂₂ = 14695687892034923894396708

A₂₁ 3,3064577752, P_{n+1 = e}^{LnPn (An  +  LnPn) / LnPn + 1}. P₂₂ = 14695687895898252945187245

[α₂₁] 0,9572300894 , ᴫ = A₂₁^α21 = 3,1415926535963569673999304719203

k₂₁ 8,2906205570, P_n+1 = (P₁^1/n + P₁^1/n k_n)ⁿ. P₂₂ = 14695688038436908598856459

ζ₂₁ 8,6385232043, P_n+1 = (P_n + P_n ζ_n). P₂₂ = 14695688039855846107963393

∆₂₁ 0,0368171907, P_n+1 = e^{ln10 Pn – ∆n}. P₂₂ = 14695687906844842565522824

σ₂₁ 61,2424540832, P_n+1 = 9·10ⁿ⁺⁵/σ_n. P₂₂ =               14695688039824771801054526

Ordenats de majors a menors

14695688141774904562112384, x₂₁

14695688039855846107963393, ζ₂₁

14695688039824771801054526, σ₂₁

14695688038436908598856459, k₂₁

14695687906844842565522824, ∆₂₁

14695687895898252945187245, A₂₁

14695687892034923894396708, β₂₁

 

6.- Tram 23, P₂₃. 10²⁷_10²⁸.

Càlculs

x₂₂ 1,0391365419, P_n+1 = P_n^x. P₂₃ = P₂₂^x22 = 141953697865294212403678616

β₂₂ 0,8188749312, P_n+1 = e^{e^(βn) + LnPn}. P₂₃ = 141953693887246608765377832

A₂₂ 3,3070833473, P_{n+1 = e}^{LnPn (An  +  LnPn) / LnPn + 1}. P₂₃ = 141953693962898668829270103

[α₂₂] 0,9570786865, ᴫ = A₂₂^α22 = 3,1415926537031071918847122459146

k₂₂ 8,3070801334, P_n+1 = (P₁^1/n + P₁^1/n k_n)ⁿ. P₂₃ = 141953696781526583377785416

ζ₂₂ 8,6595475088, P_n+1 = (P_n + P_n ζ_n). P₂₃ = 141953696795491493383293968

∆₂₂ 0,0346382876, P_n+1 = e^{ln10 Pn – ∆n}. P₂₃ = 141953694067950593506269018

σ₂₂ 63,4009554044, P_n+1 = 9·10ⁿ⁺⁵/σ_n. P₂₃ = 141953696795165388534527860

Ordenats de majors a menors

141953697865294212403678616, x₂₂

141953696795491493383293968, ζ₂₂

141953696795165388534527860, σ₂₂

141953696781526583377785416, k₂₂

141953694067950593506269018, ∆₂₂

141953693962898668829270103, A₂₂

141953693887246608765377832, β₂₂

 

7.- Tram 24, P₂₄. 10²⁸_10²⁹.

Càlculs

x₂₃ 1,0377008141, P_n+1 = P_n^x. P₂₄ = P₂₃^x23 = 1374370838628871623260532656

β₂₃ 0,8198901337, P_n+1 = e^{e^(βn) + LnPn}. P₂₄ = 1374370799287458980713559517

A₂₃ 3,3079512140, P_{n+1 = e}^{LnPn (An  +  LnPn) / LnPn + 1}. P₂₃ = 1374370800119998556382713318

[α₂₃] 0,9568687693, ᴫ = A₂₃^α23 = 3,1415926534930017615857840655907

k₂₃ 8,3230676251, P_n+1 = (P₁^1/n + P₁^1/n k_n)ⁿ. P₂₄ = 1374370827469640276565818901

ζ₂₃ 8,6818248383, P_n+1 = (P_n + P_n ζ_n). P₂₄ = 1374370827523096656094735641

∆₂₃ 0,0323346931, P_n+1 = e^{ln10 Pn – ∆n}. P₂₄ = 1374370801140522181742909114

σ₂₃ 65,4845098555, P_n+1 = 9·10ⁿ⁺⁵/σ_n. P₂₄ = 1374370827522364977259228773

Ordenats de majors a menors

1374370838628871623260532656, x₂₃

1374370827523096656094735641, ζ₂₃

1374370827522364977259228773, σ₂₃

1374370827469640276565818901, k₂₃

1374370801140522181742909114, ∆₂₃

1374370800119998556382713318, A₂₃

1374370799287458980713559517, β₂₃

 

Carreres de nombre primers:

1.- Ordenats de major a menor P₁₈ (x, ∆, A, k, ζ, β, σ)

2.- Ordenats de major a menor P₁₉ (x, ∆, β, ζ, A, k, σ)

3.- Ordenats de major a menor P₂₀ (x, ∆, β, k, A, σ, ζ)

4.- Ordenats de major a menor P₂₁ (x, ∆, β, A, ζ, σ, k)

5.- Ordenats de major a menor P₂₂ (x, ζ, σ, k, ∆, A, β)

6.- Ordenats de major a menor P₂₃ (x, ζ, σ, k, ∆, A, β)

7.- Ordenats de major a menor P₂₄ (x, ζ, σ, k, ∆, A, β)

Carrers de Pi:

1.- ᴫ = A₁₇ ^α17 = 3,141592653746817318111551536395

4.- ᴫ = A₂₀ ^α20 = 3,1415926537052375616842237410935

6.- ᴫ = A₂₂ ^α22 = 3,1415926537031071918847122459146

2.- ᴫ = A₁₈ ^α18 = 3,1415926536627938166117798652309

5.- ᴫ = A₂₁ ^α21 = 3,1415926535963569673999304719203

3.- ᴫ = A₁₉ ^α19 = 3,1415926535515878544617954412875

7.- ᴫ = A₂₃ ^α23 = 3,1415926534930017615857840655907

 

RESERVA DE VARIABLES I VALORS DE PRIMERS PER TRAMS CORRESPONENTS

X

1,0406898729 x₂₁, 1,0391365419 x₂₂, 1,0377008141 x₂₃, 1,0363704250 x₂₄, 1,0351347167 x₂₅, 1,0339843735 x₂₆, 1,0329112081 x₂₇, 1,0319079877 x₂₈, 1,0309682909 x₂₉, 1,0300863901 x₃₀, 1,0292571541 x₃₁, 1,0284759664  x₃₂, 1,0277386570 x₃₃, 1,0270414449 x₃₄, 1,0263808895 x₃₅, 1,0257542274 x₃₆, 1,0251589592 x₃₇, 1,0245928187               x₃₈, 1,0240537455 x₃₉, 1,0235398621 x₄₀, 1,0230494537 x₄₁, 1,0225809504 x₄₂, 1,0221329120   x₄₃, 1,0217040147 x_44, 1,0212930770 x₄₅, 1,0208990111 x₄₆, 1,0205208145 x₄₇, 1,0201575609 x₄₈, 1,0198083939 x₄₉, 1,0194725200 x₅₀, 1,0191492029 x₅₁, 1,0188377588 x₅₂, 1,0185375513 x_53, 1,0182479917 x₅₄, 1,0179685306              x₅₅, 1,0176986558 x₅₆, 1,0174378880 x₅₇, 1,0171857794 x₅₈, 1,0169419100 x₅₉, 1,0167058866   x₆₀, 1,0164773397 x₆₁, 1,0162559224     x₆₂, 1,0160413089 x₆₃, 1,0158331924 x₆₄, 1,0156312842 x₆₅, 1,0154353117 x₆₆, 1,0152450180               x₆₇, 1,0150601604 x₆₈, 1,0148805094 x₆₉, 1,0147058482 x₇₀, 1,0145359714              x₇₁, 1,0143706844 x₇₂ …

 

Tram 22, P₂₂. 10²⁶_10²⁷. P₂₂ = P₂₁^x21 = 14695688141774904562112384, x₂₁. 26 dígits.

P₂₃ = P₂₂^x22 = 141953697865294212403678616, x₂₂

P₂₄ = P₂₃^x23 = 1374370838628871623260532656, x₂₃

P₂₅ = P₂₄^x24 = 13339154581482237970599813767, x₂₄

P₂₆ = P₂₅^x25 = 129806583834275273163610583078, x₂₅

P₂₇ = P₂₆^x26 = 1266758625570482228621904954533, x₂₆

P₂₈ = P₂₇^x27 = 12399663299473326816779993245116, x₂₇

P₂₉ = P₂₈^x28 = 121769362643040095373851516658920, x₂₈­

P₃₀ = P₂₉^x29 = 1199975304548124996132214659698100, x₂₉

P₃₁ = P₃₀^x30 = 1,1868755699351501611351626558941e+34, x₃₀

P₃₂ = P₃₁^x31 = 1,1784884056626904909967271922779e+35, x₃₁

P₃₃ = P₃₂^x32 = 1,1749386638144873940322252791689e+36, x₃₂

P₃₄ = P₃₃^x33 = 1,1763836366532272482741124683145e+37, x₃₃

P₃₅ = P₃₄^x34 = 1,1830148123929687944775285717987e+38, x₃₄

P₃₆ = P₃₅^x35 = 1,1950595020278141055888764566739e+39, x₃₅

Tram 37, P₃₇. 10⁴¹_10⁴². P₃₇ = P₃₆^x36 = 1,2128232266276392663244103495663e+40, x₃₆. 41 dígits.

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