INSTITUTE OF SCIENCE

www.instituteofscience.com

[R]

     Hydration, Periodicity & Prime Numbers.  S.H. Shakman

(1) Groups of atomic numbers (Z) with near-equal   Fig. 1: 

hydrated Z values per Flint* (Zh) correlate with    Z  Zh  MG

Mendeleev Groups(MG)** as in Fig.1 & 1a. Prime      3 183  1

Z's in Fig.1,1a (bold) include 4 of total 8 prime  29 182 

numbers in MG1, 2 of 4 in MG2, and 2 of 3 in MG7.  55 181 

(2) Symmetry of prime nos. w/in Flint's matrix is   4 175  2

highlighted when no. 89 thru 1 are superimposed on 30 174 

series 1-89; 20 of 25 primes in each series would  56 173 

be superimposed on a prime in the other, at points  5 167  3

circled in Fig.2a (89 on 1, 83 on 7, which points  31 166 

describe arcs 1-23-47-73,7-29-53-79... (Fig. 2b)   57 165 

(3) First gap exceeding five between primes(89-97) 11 119  1

(a) encompasses 92, concluding atomic number of    37 118 

   Figure 2:                  natural elements &   17  71  7 

   Flint's matrix, !=prime.   Flint periods*;      43  70 

                              (b) coincides w/the 

 0.!!!.!.!...!.!...!.!...!23  start of the "Actinides"** 

                              (89 is also Fibonacci no.); & 

23!.....!.!.....!...!.!...46  (c) foreshadows larger gap: In 

                              extended Flint's matrix as in

46.!.....!.....!.!.....!..69      Fig.2c, light from above  

                                  37-41 through 89-97 would

69..!.!.....!...!.....!.......!97  illuminate gap 113-127.  

92.....!...!.!...!.!...!..............!127 

*  FLINT, L.H., Behavior Patterns of Hydration (1964), 21. 


Figure 1b illustrates correlations between calculated hydrated 
"weights" (atomic number equivalents) and Mendeleev groups, 
suggesting the influence of gravitational attraction as underlying
Mendeleev's periodicity.

─────────────────────────────────────────────────────────────────────────────────
Figure 1b.  Hydrated Atomic‑Number‑Equiv. (Z'h)
per Flint3,4 v.s. Mendeleev Groups
─────────────────────────────────────────────────────────────────────────────────

       1          2          3          4          5        Mendeleev
    Z'h (Z)    Z'h (Z)    Z'h (Z)    Z'h (Z)    Z'h (Z)     Group

                          148(85)    212(77)   276(69)
                                 ┌─────────────┐
                85(67)    149(59)│   213(51)   │------------(V)
              ┌──────────────────┘  ┌──────────┘
              │ 86(41)    150(33)   │214(25)
┌─────────────┘                     │
│    23(23)     87(15)   151( 7)    │
└───────────────────────────────────┘
                92(92)    156(84)   220(76)
                                 ┌─────────────┐
                93(66)    157(58)│   221(50)   │------------(IV)
              ┌──────────────────┘  ┌──────────┘
              │ 94(40)    158(32)   │222(24)
┌─────────────┘                     │
│    31(22)     95(14)   159( 6)    │
└───────────────────────────────────┘
               100(91)    164(83)    228(75)
                      ┌────────────────────────┐
               101(65)│   165(57)   229(49)    │------------(III)
              ┌───────┘             ┌──────────┘
              │102(39)    166(31)   │230(23)
┌─────────────┘                     │
│    39(21)   103(13)   167( 5)     │
└───────────────────────────────────┘
               108(90)    172(82)   236(74)
                      ┌────────────────────────┐
               109(64)│   173(56)    237(48)   │------------(II)
              ┌───────┘             ┌──────────┘
      46(46)  │110(38)    174(30)   │
┌─────────────┘                     │
│    47(20)    111(12)   175( 4)    │
└───────────────────────────────────┘
               116(89)    180(81)   244(73)
                      ┌────────────────────────┐
               117(63)│   181(55)    245(47)   │------------(I)
              ┌───────┘             ┌──────────┘
     54(45)   │118(37)    182(29)   │
┌─────────────┘                     │
│    55(19)    119(11)    183( 3)   │
└───────────────────────────────────┘
               124(88)    188(80)   252(72)
                      ┌─────────────┐
               125(62)│   189(54)   │253(46)
              ┌───────┘  ┌──────────┘
     62(44)   │126(36)   │190(28)
┌─────────────┘          └──────────┐
│    63(18)   127(10)    191 (2)    │-----------------------(0)
└───────────────────────────────────┘
               132(87)    196(79)    260(71)
                      ┌─────────────┐
     69(69)    133(61)│   197(53)   │-----------------------(VII)
┌─────────────────────┘  ┌──────────┘
│    70(43)    134(35)   │198(27)
│                        │
│    71(17)    135( 9)   │199 (1)
└────────────────────────┘
               140(86)    204(78)   268(70)
                      ┌─────────────┐
     77(68)    141(60)│   205(52)   │-----------------------(VI)
┌─────────────────────┘  ┌──────────┘
│    78(42)    142(34)   │206(26)   
│                        │
│    79(16)    143( 8)   │207(0)
└────────────────────────┘                                                   
──────────────────────────────────────────────────────────────────────
Underlined Bold = Prime numbers
────────────────────────────────────────────────────────
Z    = Atomic number; Z'h  = Z + 9Hmax (Equation 3);
Hmax calculated as per eq. 2, assuming C=0 in eq. 1

Equation 1:  Z' = Z+C (Z=atomic number; C=valence)
Equation 2:  Hmax = 23n ‑ Z', when Hmax = 23 to  0, and n = 1 to 4
                                  (for Z' = 0 to 23, n=1; 
                                  for Z' = 23 to 46, n=2;
                                  for Z' = 46 to 69, n=3;
                                  for Z' = 69 to 92, n=4).

 

Figure 2a:

Note:
(1) In above Figure 2a, all prime numbers between zero and 92 are circled.
(2) To further illustrate the symmetry in this structure, as shown below,
the first half is listed in sequence and the second backwards,

with all prime numbers bold/underlined, beginning with numbers 1 and 89 juxtaposed.
(3) As shown, beyond prime number 5, all prime numbers line up in pairs:

       0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22

92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46

Quite a coincidence (at a minimum)!

  Fig. 2b:

Figure 2c:

 IOS

BOOKS

Copyright 1985

(TXu219626); 1987 (TXu271794)

S H

Shakman.  All rights reserved. 

Proposed for

1988 AAAS Meeting, AAAS # 0925.17; withdrawn 25 Sept. 1987.

[HOME]

Email:  mail@instituteofscience.com