Primes, families of, arranged in sets of primeth recursions --

Initial primes of such sets :-

ord.

card.

prod.

1st

2

2

2nd

7

14

3rd

13

39

4th

19

76

5th

23

115

6th

29

174

7th

37

259

8th

43

344

9th

47

423

10th

53

530

11th

61

671

12th

71

852

13th

73

949

14th

79

1106

15th

89

1335

16th

97

1552

17th

101

1717

18th

103

1824

19th

107

1963

20th

113

2260

[note the years 1963 (JFK) and (in the Coptic calendar) 1717 (WTC).]

2; 7; 13; 19; 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, ...

(These primeth-recursion sets are :-

2, 3, 5, 11, 31, 127, 709, ...;

7, 17, 59, 277, ...;

13, 41, 179, ...;

19, 67, 331, ...;

23, 83, 431, ...;

29, 109, ...;

37, 157, ...;

43, 191, ...;

47, 221, ...;

53, 241, ...;

61, 283, ...;

71, 353, ...;

73, 367, ...;

79, 401, ...;

89, 461, ...;

97, 509, ...,

101, 547, ...

103, 563, ...;

107, 587, ...;

113, 617, ...;

...)

19

(Stated in terms to the base of the initial prime of each such set, the sets are :-

2, 2+1 (=2^2-1), 2^2+1, 2^3+2+1, 2^4+2^3+2^2+2+1 (=2^5-1), 2^7+2^6+2^5+2^4+2^3+2^2+2+1 (=2^8-1), 2^9+2^7+2^6+2^2+1, ... [the 2nd is 2^2-1; the 5th is 2^5-1; the 6th is 2^8-1]

7, 7*2+3, 7^2+7+3, (7^2)*5+7*4+4 (= 7^3-7^2-7*3-3), ...

13, 13*3+2, 13^2+10, ...

19, 19*3+10, ...

[written Dec 26th Mon 2011]

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[found, two days later, in The On-Line Encyclopedia of Integer Sequences http://oeis.org ]

A007821 Primes p(n) where n runs through the nonprimes. +100

25

2, 7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373

A088982 Primes that are between consecutive prime-indexed-primes. +90

0

7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 389

The ordinals of these primes are listed at http://oeis.org/A007821/b007821.txt

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[written Jan 5 (Thur) 2012]

N.B. 13 * 220 = 2260 = 2012 (praedicted year of mass-landings of the UFOs) + 248 :-"the Torah ... contains two hundred and forty-eight commandments, corresponding to the number of the members of thy body" (Ginzberg, Legends of the Jews, p. 384).

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