---------------------------------------------------------
Elemental(2f0+1,f0=1) = 100 -- shifted to align with f0 --> 100
Pat(2n+1,n=1) = 100
Size = 3
Number of 1's = 1; 1/3 = 0.3333333333333333
Number of 0's = 2; 2/3 = 0.6666666666666666
Total Candidates= 1
Singleton Candidates = 0; 0/1 = 0.0
Twin Candidates = 1; 1/1 = 1.0
---------------------------------------------------------
---------------------------------------------------------
Elemental(2f0+1,f0=2) = 10000 -- shifted to align with f0 --> 01000
Pat(2n+1,n=2) = 110100100101100
Size = 15
Number of 1's = 7; 7/15 = 0.4666666666666667
Number of 0's = 8; 8/15 = 0.5333333333333333
Total Candidates= 5
Singleton Candidates = 2; 2/5 = 0.4
Twin Candidates = 3; 3/5 = 0.6
---------------------------------------------------------
---------------------------------------------------------
Elemental(2f0+1,f0=3) = 1000000 -- shifted to align with f0 --> 0010000
Pat(2n+1,n=3) = 11110010010110011010010110110011010011010110111010010010111011010110010110011011010010110011010010011
1100
Size = 105
Number of 1's = 57; 57/105 = 0.5428571428571428
Number of 0's = 48; 48/105 = 0.45714285714285713
Total Candidates= 33
Singleton Candidates = 18; 18/33 = 0.5454545454545454
Twin Candidates = 15; 15/33 = 0.45454545454545453
---------------------------------------------------------
---------------------------------------------------------
Elemental(2f0+1,f0=5) = 10000000000 -- shifted to align with f0 --> 00001000000
Pat(2n+1,n=4) = 11111010010110011010010110110011010011010110111010010010111111010110011110011011010010110011110010011
1110111100100101100110101101101100110100110101101110100101101110110111100101100110110100101100110100
1101111001111001001011011101001011111001101001101011011111001001011101101011001011001101111001011001
1010010011110011110010110110011011010110110011010011010110111010011010111011010110010110111011010011
1100110100100111100111100100101110110100101101100110101110101101110100100101110110101101101100110110
1001011001101001001111001111001101011001101001011011011101001101111011101001001011101111011001011101
1011010010110011010110011110011110010010110011010010110110011011011010110111010010010111011010111010
1100110110100101101110100100111100111100100101100111100101101110110100110101101110101100101110110101
1001011001101101011011001101101001111001111001001011001101001111011001101001101011011101001001111101
1010110010110011111010010111011010010011110011110110010110011010010110110011010011110110111011010010
1110110101100101100110110110101100110100100111101111100100111100110100101101100111100110101111110100
100101110110101100101100110110100101100110100101111100
Size = 1155
Number of 1's = 675; 675/1155 = 0.5844155844155844
Number of 0's = 480; 480/1155 = 0.4155844155844156
Total Candidates= 345
Singleton Candidates = 210; 210/345 = 0.6086956521739131
Twin Candidates = 135; 135/345 = 0.391304347826087
---------------------------------------------------------
---------------------------------------------------------
Elemental(2f0+1,f0=6) = 1000000000000 -- shifted to align with f0 --> 0000010000000
Pat(2n+1,n=5) = 11111110010110011010010110110011010011010110111010010010111111010110011110011011010110110011110010011
1110111110100101100111101101101100110100110101111110100101101110110111100101100110110110101100110101
1101111001111001001011011101001011111011101001101011011111001001111101101011011011001101111001011001
1011010011110011110010110110011011010110111011010011010110111010011010111011010111010110111011110011
1100110100100111100111100100101111110100101101100110101110111101110100101101110110101101101100110110
1001011001111001001111001111001101011101101001011011011101001101111011101001101011101111011001011101
1011010010110011010110011110111110010010110011010010111110011011011110110111010010010111011011111010
1100111110100101101110100100111110111100100101100111100101101110110100110101101110101100101110110101
1001011001101101011011011101101001111001111001001111001101001111011001101001101011011101101001111101
1110110010110011111010010111011010010011110011110110010110011010011110110011010111110110111011010010
1110110101100101101110110110101100110100100111101111100101111100110100101101100111110110101111111100
1001011101101011001011101101101001011001101001011111001111101101011001101011011011001101001101011011
1010010010111111010110011110011011010011110011110010111111011110010010110011011110110110011110011010
1101110100101101110110111100101100110110100101100110100110111100111101100101101110100101111100110100
1101011011111001001011101101011001111001101111011011001101001001111001111101011011001111101011011001
1010011010111111010011010111011010110010110111011011011110011010110011110011110010010111011010010110
1101110101110101101110100100111110110101101101100110110100101100110110100111100111100110101100110100
1011011111101001101111011101001001011101111011101011101101111001011001101011001111001111001001011011
1010010110110011011011011110111010010110111011010111010110011011010010110111110010011110011110010010
1110111100101101110110100110101101110101110101110110101100101100110110101101100110110100111101111100
1001011001101001111111001101001111011011101001001111101101111001011001111101001011101101001001111101
1110110010110011010010110110011010011110110111011110010111011010110010110011011011010110111010010011
1101111100100111100110100101101100111100110101111110110100101110111101100101100110110100101110110100
1011111001111101001011001101001111011001101011101011011101001001011111101011001111011101101001011001
1110010011111011110010110110011010110110110011011011010110111110010110111011011110010111011011010010
1100110100110111100111100110101101110101101111100110100110101101111100100101111110101100101100110111
1001111001101001011111001111001011011001101101011011001111001101011011101001101011101101011001011011
1011010011110011010011011110011110110010111011010010110110011010111010110111010010010111011010110111
1100110110101101100110100100111100111110110101100111100101101101110100110111111110100100101110111101
1001011101101101101011001101011001111001111001001011001101001011011011101101101011011101001001111101
1010111110110011011010010110111011010011110011110010010110011110010110111011010011010110111010110010
1110110101110101100110111101101100110110100111100111100100101101110100111101100110100110111101110100
1011111101101011001011001111101001011101111001001111001111011001011101101001011011001101001111011011
1011011010111011010110010110011011011010110011010010011110111110010011110011010010111110011110011110
1111110100100101110110111100101100111110100101100110100101111110111110100101100110100101101100110100
1101011011101011001011111101011001111001101101001011011111001001111101111001001111001101011011011001
1010011010110111011010110111011111110010110011011010010111011010011011110011110010010110111010011111
1100110101110101101111100100101110110101100101101110111100101100110100100111100111100101101100110110
1011011001101101101011011111001101011101101011001011111101101001111001101001001111001111001101011101
1010110110110011010111010110111010010010111111010110110110011011010011110011010010111110011110011010
1100110110101101101111100110111101110100100101110111101100101110110110100101100110101110111100111101
1001011001101001011011001101101101011011101001001011101101011101111001101101011011011101001001111001
1111010010110011110010110111011010011010111111010110010111011010110010110011011011110110011011110011
1100111100100101100110100111101101110100110101101110100100111110110101101101100111110100101110110110
1001111001111011001011001101001011011101101001111011011101101001011101101011101011001101111101011001
1010010011110111110010011110111010010110110011110011011111111010010110111011010110010110011011010010
1100111100101111100111110100101110110100101101100110100110101101110100110101111110101100111100110110
1001011001111001001111111111001001011001101011011111001101001111011011101001011011101101111001011001
1111010010110011010011011111011110010010110111010010111110011010011010110111110110010111011010110010
1100110111100101101110100100111100111100101111100110110101101100110100110101101110110110101110111101
1001011011101101001111101101001001111001111001001011101101001111011001101011101011011101001001011101
1010110110110111011010010110011010010011110011110011110110011010010110110111011011011110111110010010
1110111101100101110110110100101100110101100111100111100110101100110101101101100110110110101101110100
1001011111101011101011001101101001111011101001011111001111001001011001111101011011101111001101011011
1010110010111011010110010110011011010110110011011011011110011110110010110011010011110110011010011010
1101110100100111110110101100111100111110101101110110100100111100111111100101100111100101101100110100
1111011111101101001011101101011001011001101101101011001101011001111011111001001111001101001011011011
1110011010111111010010011111011010110110110011011010010110011011010111110011111010010110011010010110
1110110100110101101110100100101111110101110111100110111100101100111100100111110111100100101101110101
1011011001101001101111011101001011011101101111001011001101101001011001111001101111001111001001011111
1010010111110011010011010110111110011010111011010110010110011011110010110011010010011110111110010110
1100110110101111100110100111101101110100110101110110111100101101111110100111100110100100111110111100
1001011101101001011011001101011101011011101011001011101101011011011001101101001011011101001001111001
1110011011110011010010110110111010011011110111011010010111011110110010111011011010010111011010110011
1100111100100101100110100111101100110111110101101110100100101110110101110101101110110100101101110100
1001111001111001011011001111001011011101101101101011011111011001011101101011001011101101101011011001
1011010011110011110011010110011010111110110011010011010110111010010011111111010110010110011111010011
1110110100101111100111101100101100110110101101100111100111101101110110100101110110101100101100110110
1101011001101001101111011111011001111001101001011011001111001101011111101001001011101101011001111001
1011010110110011010010111110011111010010110011110010110110011010011010111111010010010111111010110011
1100110110110101100111101100111110111100100101100110101101101101110100110101101110100101111110110111
1011011001101101001011001101101101111001111001001011011101001011111101101001101011011111001001011101
1010111010110011011110010110011010010011110011110010110110111011010110110011010011011110111010011110
1110110101100101101110110100111100111100100111100111100100101110110100101101100110101110101101110100
1101011101101011011011001101101001011001101001001111011111001101011001101001011111011101001111111011
1010010010111011111110010111011111010010110011010110011111011110010010110011010010110110011011011010
1101110101100101110110101110101100110110100101101110100100111100111100100111100111100101101110110100
1101011011101111001011101111011001011001101101011011101101101001111001111001001011001101001111011001
1010111010110111010010011111011010110010110111111010010111011010010011110011110110110110011010010110
1100110110111101101111110100101110110101100101110110110110101100110100100111101111100110111100110101
1011011001111001101011111101001001011111101011001011001101101001111001101001011111001111101001011001
1011010110110011110011010110111010010010111111010110011110011011010010110011110011011111011110110010
1100110101101101100110100110101101110100101101110110111100111100110110101101100110100110111100111110
1001011011111001011111001101001101011111111001001011101101011001011001101111101011001101011001111001
1110010110110011011010110110111010011010110111010011011111011010110110110111011010011110011011010011
1100111100100101110110100101101110110101110101101110100100101110110101111101100110111100101100110100
1001111001111001101011011101001011011011101001101111011101001011011101111011001011101101101001011001
1110110011110011110010010111011010010110110011011011010110111010011010111011010111010110011011010010
1101110100100111101111100100101100111100101111110110100111101101110101100101110110111100101100111110
1011011001101101001111101111001001011001101001111011001101001101011011101011001111101101011001011001
1111010010111111010010011110011110110011110011010010110110011010011110110111011010010111011110110010
1100110110110101110110100100111101111100100111100110100111101100111101110101111110100100101110110101
1001011011101101001011001101001011111001111101011011001101001011011001101101101011011111001001011111
1010110011111011011010010110011110010011111011110011010110011010110110110011010011010110111010010110
1111110111100101100110110100111100110100111111100111100100101101110110101111100111100110101101111100
1001011101101011001011001101111001011001101001101111001111011011011001101101011011001101001101011011
1010011010111011010110011110111011010111110011010010011110011111010010111011110010110110011010111010
1111110100100101110110101101101100110110110101100110101100111100111100110101100110100101101101110100
1101111011101001001111101111011011011101101101001011001101111001111001111001001011001101001011011101
1011011010110111010010010111011010111010110011011110010110111010010011110011110010010110111110010110
1110110100110111101110101101101110110101100101100110110101101100111110100111100111100100101110110100
1111011001101001101011011101001101111101101011001011001111101001011101101001001111011111011001011001
1010010111110011010011110110111011010010111011011110010110011111011010110011010010011111111110010011
1100110100101101100111100110101111110101100101110110101100101100110110100101101110100101111100111110
1001111001101001011011001101001101011011101101001011111111011001111001101101001011101111001001111101
1110010010110011010111110110011010111010110111010010110111011011110010110111011010010110011010011011
1100111100101101101110100101111100110110110101101111100100101110110101100101110110111100101100110100
1001111001111001111011001101111011011001101001101011011101001101011111101011001011011101101001111001
1010010111110011110010010111011011010110110011110111010110111010010010111011010110110110011011010010
1100110100110111100111101110101100110100101101101110100110111101110100100101110111101100111110110110
1011011001101011001111001111101001011001111001011011001101101101011111101001001011101101011101011001
1011011010110111010110011110011110010010110011110010110111111010011010110111010110011111011010110110
1100110110101101100110110100111100111100100101100110100111101110110100110101101110100100111110110101
1101011001111111001011101101001001111001111011001011011101001011011001101001111111011101101011011101
1010110010110011011011010110011110010011110111110010011111011010010110110011110011010111111010011010
1110110101100101100110110100101100110100101111101111110100101100110100101111100110100111101101110100
1001011111101111001111001111101001011001111001001111101111001001011001101011011011001101001101011011
1010110110111011011110010110011011010010110111010011011110011110010011110111010010111110011010011010
1101111110100101110111101100101100110111100101110110100100111100111100101101100110110111101100110101
1101011011101001101011101101011001011011101101001111001101001001111001111001011011101101001011011001
1011111010110111110010010111011010110110111011011010010110011010010011110011110011010110011010110110
1101110100110111101110100100101111111101100101110110110100111100110101101111100111100100101100110110
1011011001111101101011011101001001011101101011101011001101101001011011101001101111001111011001011001
1110010110111011010011010110111010110010111011010110011110011011010110110011011010011110011111010010
1100111100111101100110100110101111110100100111110110101100101100111110110101110110101100111100111101
1001011001101001011011011101001111011011101101001111101101011011011001101101101011001101101001111011
1110010011110011010010110111011110011010111111010010010111011010111010110011011110010110011010010111
1100111110100101101110100101101100110100110111101110100101101111110101100111100110110100101100111100
1001111101111001001011101101011011011001101001101011011101001111011101101111001011001101101001011001
1010011011110111110010010110111010010111110011010011110110111110010010111011011110010110011111110010
1100110100100111110111100101101100110110101101100110100110101101110101110101110110101100101101110110
1001111011101001001111001111001001111101101001011011001101011101011011101101001011101111011011011001
1011010010111011010010011110011110011010110011010011110110111010111011110111010010010111011110110010
1111110110100101100110101100111100111100101101100110100101101100110110110101101111100100101110110101
1101011101101101001011011101001001111001111001101011001111011011011101101001101011011101011001011111
1010110010110011011010111110011011010111110011110010010110011011011110110011110011010110111010010011
1110110101100101100111110100101110110100110111100111101100101100110100101101100110100111101101110110
1001011101101011001111001101101111011001101001001111011111101001111001111001011011001111001101011111
1010010010111011010110010110011011011010110011010110111110011111010010110011010010110110111010011010
1101110100100111111110101101111100110110100101100111110100111110111100100101100110101101101110110100
1101011011101001011011101101111101011001101111001011001101001101111001111001001011011101001011111001
1010011011110111110010110111011010110010110011011110010110011110010011110011110010110111011011010110
1100110100110101101110100110101110110101100101101110110100111100110100100111101111100100101110110100
1011111001101011111011011101001001011101101111011011001111101001011001101001001111101111001101011001
1010010110110111010011011110111010110010111011110110010111011011010010110111010110011110011110010011
1100110100101101100110110110101101110110100101110111101110101100110110100101111110100100111100111100
1001011001111001111011101101011101011011101011001011101101011001011011101101011011001101101001111001
1110010110110011010011110110011011011010110111110010011111011010110010111011111010010111011010010011
1100111101110101100110101101101100110100111101101110110100101111110101100101100110110110111100110100
1011111011111001001111001101101011011001111001101011111101001001011101101011001011001101101001011001
10100111111100
Size = 15015
Number of 1's = 9255; 9255/15015 = 0.6163836163836164
Number of 0's = 5760; 5760/15015 = 0.3836163836163836
Total Candidates= 4275
Singleton Candidates = 2790; 2790/4275 = 0.6526315789473685
Twin Candidates = 1485; 1485/4275 = 0.3473684210526316
---------------------------------------------------------
---------------------------------------------------------
Elemental(2f0+1,f0=8) = 10000000000000000 -- shifted to align with f0 --> 00000001000000000
Pat(2n+1,n=6) = TOO BIG!
Size = 255255
Number of 1's = 163095; 163095/255255 = 0.6389492860081095
Number of 0's = 92160; 92160/255255 = 0.3610507139918905
Total Candidates= 69885
Singleton Candidates = 47610; 47610/69885 = 0.6812620734063104
Twin Candidates = 22275; 22275/69885 = 0.31873792659368966
---------------------------------------------------------
---------------------------------------------------------
Elemental(2f0+1,f0=9) = 1000000000000000000 -- shifted to align with f0 --> 0000000010000000000
Pat(2n+1,n=7) = TOO BIG!
Size = 4849845
Number of 1's = 3190965; 3190965/4849845 = 0.6579519551655775
Number of 0's = 1658880; 1658880/4849845 = 0.3420480448344225
Total Candidates= 1280205
Singleton Candidates = 901530; 901530/1280205 = 0.7042075292628915
Twin Candidates = 378675; 378675/1280205 = 0.2957924707371085
---------------------------------------------------------
---------------------------------------------------------
Elemental(2f0+1,f0=11) = 10000000000000000000000 -- shifted to align with f0 --> 00000000001000000000000
Pat(2n+1,n=8) = TOO BIG!
Size = 111546435
Number of 1's = 75051075; 75051075/111546435 = 0.6728236092888132
Number of 0's = 36495360; 36495360/111546435 = 0.32717639071118676
Total Candidates= 28543185
Singleton Candidates = 20591010; 20591010/28543185 = 0.7213984704229749
Twin Candidates = 7952175; 7952175/28543185 = 0.2786015295770251
---------------------------------------------------------
IT IS ALSO POSSIBLE TO ALGORITHMICALLY DETERMINE THE # OF ONES AND ZEROS AS OUTLINED ON MY WEBSITE.
n=2; Ones->7 Zeros->8 zeros/(ones+zeros) = 0.5333333333333333
n=3; Ones->57 Zeros->48 zeros/(ones+zeros) = 0.45714285714285713
n=4; Ones->675 Zeros->480 zeros/(ones+zeros) = 0.4155844155844156
n=5; Ones->9255 Zeros->5760 zeros/(ones+zeros) = 0.3836163836163836
n=6; Ones->163095 Zeros->92160 zeros/(ones+zeros) = 0.3610507139918905
n=7; Ones->3190965 Zeros->1658880 zeros/(ones+zeros) = 0.3420480448344225
n=8; Ones->75051075 Zeros->36495360 zeros/(ones+zeros) = 0.32717639071118676
n=9; Ones->2212976535 Zeros->1021870080 zeros/(ones+zeros) = 0.3158944462039045
n=10; Ones->69624142665 Zeros->30656102400 zeros/(ones+zeros) = 0.30570430277797206
n=11; Ones->2606749381005 Zeros->1103619686400 zeros/(ones+zeros) = 0.2974420243245134
n=12; Ones->107980344307605 Zeros->44144787456000 zeros/(ones+zeros) = 0.2901873408044033
n=13; Ones->4687299592683015 Zeros->1854081073152000 zeros/(ones+zeros) = 0.28343879799499855
n=14; Ones->222157161929253705 Zeros->85287729364992000 zeros/(ones+zeros) = 0.27740818527170075
---------------------------------------------------------
COMPARE THE ABOVE VALUES TO THE NUMBER OF PRIMES/ODD BETWEEN P(n)->P(n)^2
NOTE: P(n)->P(n)^2 compares to n-1 above because (Pat(n-1)) is in effect between P(n)->P(n)^2)
P(1)->P(1)^2 : 3->9 numPrime/numOdd = 2/2 = 1.0
P(2)->P(2)^2 : 5->25 numPrime/numOdd = 6/9 = 0.6666666666666666
P(3)->P(3)^2 : 7->49 numPrime/numOdd = 11/20 = 0.55
P(4)->P(4)^2 : 11->121 numPrime/numOdd = 25/54 = 0.46296296296296297
P(5)->P(5)^2 : 13->169 numPrime/numOdd = 33/77 = 0.42857142857142855
P(6)->P(6)^2 : 17->289 numPrime/numOdd = 54/135 = 0.4
P(7)->P(7)^2 : 19->361 numPrime/numOdd = 64/170 = 0.3764705882352941
P(8)->P(8)^2 : 23->529 numPrime/numOdd = 90/252 = 0.35714285714285715
P(9)->P(9)^2 : 29->841 numPrime/numOdd = 136/405 = 0.3358024691358025
P(10)->P(10)^2 : 31->961 numPrime/numOdd = 151/464 = 0.3254310344827586
P(11)->P(11)^2 : 37->1369 numPrime/numOdd = 207/665 = 0.3112781954887218
P(12)->P(12)^2 : 41->1681 numPrime/numOdd = 250/819 = 0.3052503052503053
P(13)->P(13)^2 : 43->1849 numPrime/numOdd = 269/902 = 0.2982261640798226
P(14)->P(14)^2 : 47->2209 numPrime/numOdd = 314/1080 = 0.29074074074074074
P(15)->P(15)^2 : 53->2809 numPrime/numOdd = 393/1377 = 0.28540305010893247
P(16)->P(16)^2 : 59->3481 numPrime/numOdd = 470/1710 = 0.27485380116959063
P(17)->P(17)^2 : 61->3721 numPrime/numOdd = 501/1829 = 0.273920174958994
P(18)->P(18)^2 : 67->4489 numPrime/numOdd = 590/2210 = 0.2669683257918552
P(19)->P(19)^2 : 71->5041 numPrime/numOdd = 655/2484 = 0.2636876006441224
P(20)->P(20)^2 : 73->5329 numPrime/numOdd = 684/2627 = 0.26037304910544345
P(21)->P(21)^2 : 79->6241 numPrime/numOdd = 789/3080 = 0.25616883116883116
P(22)->P(22)^2 : 83->6889 numPrime/numOdd = 863/3402 = 0.2536743092298648
P(23)->P(23)^2 : 89->7921 numPrime/numOdd = 976/3915 = 0.24929757343550446
P(24)->P(24)^2 : 97->9409 numPrime/numOdd = 1138/4655 = 0.24446831364124597
P(25)->P(25)^2 : 101->10201 numPrime/numOdd = 1226/5049 = 0.24282036046741928
P(26)->P(26)^2 : 103->10609 numPrime/numOdd = 1267/5252 = 0.24124143183549124
P(27)->P(27)^2 : 107->11449 numPrime/numOdd = 1353/5670 = 0.23862433862433863
P(28)->P(28)^2 : 109->11881 numPrime/numOdd = 1394/5885 = 0.2368734069668649
P(29)->P(29)^2 : 113->12769 numPrime/numOdd = 1493/6327 = 0.23597281492018335
P(30)->P(30)^2 : 127->16129 numPrime/numOdd = 1846/8000 = 0.23075
P(31)->P(31)^2 : 131->17161 numPrime/numOdd = 1944/8514 = 0.22832980972515857
P(32)->P(32)^2 : 137->18769 numPrime/numOdd = 2108/9315 = 0.2263016639828234
P(33)->P(33)^2 : 139->19321 numPrime/numOdd = 2156/9590 = 0.22481751824817517
P(34)->P(34)^2 : 149->22201 numPrime/numOdd = 2454/11025 = 0.22258503401360544
P(35)->P(35)^2 : 151->22801 numPrime/numOdd = 2511/11324 = 0.2217414341222183
P(36)->P(36)^2 : 157->24649 numPrime/numOdd = 2692/12245 = 0.2198448346263781
P(37)->P(37)^2 : 163->26569 numPrime/numOdd = 2877/13202 = 0.21792152704135737
P(38)->P(38)^2 : 167->27889 numPrime/numOdd = 3004/13860 = 0.21673881673881673
P(39)->P(39)^2 : 173->29929 numPrime/numOdd = 3201/14877 = 0.21516434765073603
P(40)->P(40)^2 : 179->32041 numPrime/numOdd = 3395/15930 = 0.21311989956057753
P(41)->P(41)^2 : 181->32761 numPrime/numOdd = 3470/16289 = 0.21302719626741973
P(42)->P(42)^2 : 191->36481 numPrime/numOdd = 3825/18144 = 0.21081349206349206
P(43)->P(43)^2 : 193->37249 numPrime/numOdd = 3901/18527 = 0.210557564635397
P(44)->P(44)^2 : 197->38809 numPrime/numOdd = 4044/19305 = 0.2094794094794095
P(45)->P(45)^2 : 199->39601 numPrime/numOdd = 4118/19700 = 0.20903553299492386
P(46)->P(46)^2 : 211->44521 numPrime/numOdd = 4580/22154 = 0.20673467545364269
P(47)->P(47)^2 : 223->49729 numPrime/numOdd = 5058/24752 = 0.20434712346477052
P(48)->P(48)^2 : 227->51529 numPrime/numOdd = 5225/25650 = 0.2037037037037037
P(49)->P(49)^2 : 229->52441 numPrime/numOdd = 5306/26105 = 0.20325608121049607
P(50)->P(50)^2 : 233->54289 numPrime/numOdd = 5471/27027 = 0.20242720242720244
P(51)->P(51)^2 : 239->57121 numPrime/numOdd = 5740/28440 = 0.20182841068917018
P(52)->P(52)^2 : 241->58081 numPrime/numOdd = 5829/28919 = 0.20156298627200112
P(53)->P(53)^2 : 251->63001 numPrime/numOdd = 6266/31374 = 0.19971951297252502
P(54)->P(54)^2 : 257->66049 numPrime/numOdd = 6540/32895 = 0.19881440948472412
P(55)->P(55)^2 : 263->69169 numPrime/numOdd = 6813/34452 = 0.1977533960292581
P(56)->P(56)^2 : 269->72361 numPrime/numOdd = 7104/36045 = 0.1970869746150645
P(57)->P(57)^2 : 271->73441 numPrime/numOdd = 7194/36584 = 0.19664334135141046
P(58)->P(58)^2 : 277->76729 numPrime/numOdd = 7485/38225 = 0.1958142576847613
P(59)->P(59)^2 : 281->78961 numPrime/numOdd = 7683/39339 = 0.19530237169221384
P(60)->P(60)^2 : 283->80089 numPrime/numOdd = 7781/39902 = 0.1950027567540474
P(61)->P(61)^2 : 293->85849 numPrime/numOdd = 8292/42777 = 0.19384248544778737
P(62)->P(62)^2 : 307->94249 numPrime/numOdd = 9026/46970 = 0.19216521183734298
P(63)->P(63)^2 : 311->96721 numPrime/numOdd = 9245/48204 = 0.19178906314828645
P(64)->P(64)^2 : 313->97969 numPrime/numOdd = 9351/48827 = 0.1915128924570422
P(65)->P(65)^2 : 317->100489 numPrime/numOdd = 9565/50085 = 0.19097534191873813
P(66)->P(66)^2 : 331->109561 numPrime/numOdd = 10348/54614 = 0.1894752261324935
P(67)->P(67)^2 : 337->113569 numPrime/numOdd = 10688/56615 = 0.188783891194913
P(68)->P(68)^2 : 347->120409 numPrime/numOdd = 11266/60030 = 0.18767283025154088
P(69)->P(69)^2 : 349->121801 numPrime/numOdd = 11390/60725 = 0.1875668999588308
P(70)->P(70)^2 : 353->124609 numPrime/numOdd = 11630/62127 = 0.18719719284691036
P(71)->P(71)^2 : 359->128881 numPrime/numOdd = 11992/64260 = 0.18661686896981014
P(72)->P(72)^2 : 367->134689 numPrime/numOdd = 12480/67160 = 0.18582489577129244
P(73)->P(73)^2 : 373->139129 numPrime/numOdd = 12860/69377 = 0.185364025541606
P(74)->P(74)^2 : 379->143641 numPrime/numOdd = 13239/71630 = 0.18482479408069244
P(75)->P(75)^2 : 383->146689 numPrime/numOdd = 13490/73152 = 0.18441054243219598
P(76)->P(76)^2 : 389->151321 numPrime/numOdd = 13883/75465 = 0.18396607698933282
P(77)->P(77)^2 : 397->157609 numPrime/numOdd = 14412/78605 = 0.18334711532345271
P(78)->P(78)^2 : 401->160801 numPrime/numOdd = 14673/80199 = 0.18295739348370926
P(79)->P(79)^2 : 409->167281 numPrime/numOdd = 15203/83435 = 0.18221369928687
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EXAMINING THE #P[P(n)->P(n)^2] AND #P_Corrected[P(n)->P(n)^2] FORMULAE
#P[P(2)->P(2)^2] = 7; #P_Corrected[P(2)->P(2)^2] = 7; actual number primes in this interval = 6
#P[P(3)->P(3)^2] = 11; #P_Corrected[P(3)->P(3)^2] = 11; actual number primes in this interval = 11
#P[P(4)->P(4)^2] = 25; #P_Corrected[P(4)->P(4)^2] = 25; actual number primes in this interval = 25
#P[P(5)->P(5)^2] = 32; #P_Corrected[P(5)->P(5)^2] = 32; actual number primes in this interval = 33
#P[P(6)->P(6)^2] = 52; #P_Corrected[P(6)->P(6)^2] = 52; actual number primes in this interval = 54
#P[P(7)->P(7)^2] = 62; #P_Corrected[P(7)->P(7)^2] = 61; actual number primes in this interval = 64
#P[P(8)->P(8)^2] = 87; #P_Corrected[P(8)->P(8)^2] = 86; actual number primes in this interval = 90
#P[P(9)->P(9)^2] = 133; #P_Corrected[P(9)->P(9)^2] = 131; actual number primes in this interval = 136
#P[P(10)->P(10)^2] = 147; #P_Corrected[P(10)->P(10)^2] = 145; actual number primes in this interval = 151
#P[P(11)->P(11)^2] = 204; #P_Corrected[P(11)->P(11)^2] = 201; actual number primes in this interval = 207
#P[P(12)->P(12)^2] = 244; #P_Corrected[P(12)->P(12)^2] = 240; actual number primes in this interval = 250
#P[P(13)->P(13)^2] = 262; #P_Corrected[P(13)->P(13)^2] = 258; actual number primes in this interval = 269
#P[P(14)->P(14)^2] = 306; #P_Corrected[P(14)->P(14)^2] = 301; actual number primes in this interval = 314
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EXAMINING THE #P[P(n-1)^2->P(n)^2] FORMULA
#P[P(1)^2->P(2)^2] = 4; #P_Corrected[P(1)^2->P(2)^2] = 4; actual number primes in this interval = 5
#P[P(2)^2->P(3)^2] = 5; #P_Corrected[P(2)^2->P(3)^2] = 5; actual number primes in this interval = 6
#P[P(3)^2->P(4)^2] = 15; #P_Corrected[P(3)^2->P(4)^2] = 15; actual number primes in this interval = 15
#P[P(4)^2->P(5)^2] = 9; #P_Corrected[P(4)^2->P(5)^2] = 9; actual number primes in this interval = 9
#P[P(5)^2->P(6)^2] = 22; #P_Corrected[P(5)^2->P(6)^2] = 22; actual number primes in this interval = 22
#P[P(6)^2->P(7)^2] = 12; #P_Corrected[P(6)^2->P(7)^2] = 11; actual number primes in this interval = 11
#P[P(7)^2->P(8)^2] = 27; #P_Corrected[P(7)^2->P(8)^2] = 26; actual number primes in this interval = 27
#P[P(8)^2->P(9)^2] = 49; #P_Corrected[P(8)^2->P(9)^2] = 47; actual number primes in this interval = 47
#P[P(9)^2->P(10)^2] = 18; #P_Corrected[P(9)^2->P(10)^2] = 16; actual number primes in this interval = 16
#P[P(10)^2->P(11)^2] = 61; #P_Corrected[P(10)^2->P(11)^2] = 58; actual number primes in this interval = 57
#P[P(11)^2->P(12)^2] = 45; #P_Corrected[P(11)^2->P(12)^2] = 41; actual number primes in this interval = 44
#P[P(12)^2->P(13)^2] = 24; #P_Corrected[P(12)^2->P(13)^2] = 20; actual number primes in this interval = 20
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EXAMINING THE #Twins[P(n)->P(n)^2] AND #Twins_Corrected[P(n)->P(n)^2] FORMULAE
#Twins[P(2)->P(2)^2] = 3; #Twins_Corrected[P(2)->P(2)^2] = 3; actual number twins in this interval = 3
#Twins[P(3)->P(3)^2] = 4; #Twins_Corrected[P(3)->P(3)^2] = 4; actual number twins in this interval = 4
#Twins[P(4)->P(4)^2] = 8; #Twins_Corrected[P(4)->P(4)^2] = 8; actual number twins in this interval = 8
#Twins[P(5)->P(5)^2] = 9; #Twins_Corrected[P(5)->P(5)^2] = 9; actual number twins in this interval = 9
#Twins[P(6)->P(6)^2] = 13; #Twins_Corrected[P(6)->P(6)^2] = 13; actual number twins in this interval = 16
#Twins[P(7)->P(7)^2] = 15; #Twins_Corrected[P(7)->P(7)^2] = 15; actual number twins in this interval = 17
#Twins[P(8)->P(8)^2] = 20; #Twins_Corrected[P(8)->P(8)^2] = 20; actual number twins in this interval = 21
#Twins[P(9)->P(9)^2] = 29; #Twins_Corrected[P(9)->P(9)^2] = 29; actual number twins in this interval = 29
#Twins[P(10)->P(10)^2] = 31; #Twins_Corrected[P(10)->P(10)^2] = 31; actual number twins in this interval = 30
#Twins[P(11)->P(11)^2] = 41; #Twins_Corrected[P(11)->P(11)^2] = 41; actual number twins in this interval = 41
#Twins[P(12)->P(12)^2] = 48; #Twins_Corrected[P(12)->P(12)^2] = 47; actual number twins in this interval = 48
#Twins[P(13)->P(13)^2] = 50; #Twins_Corrected[P(13)->P(13)^2] = 49; actual number twins in this interval = 50
#Twins[P(14)->P(14)^2] = 58; #Twins_Corrected[P(14)->P(14)^2] = 57; actual number twins in this interval = 61
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EXAMINING THE #Triplets[P(n)->P(n)^2] AND #Triplets_Corrected[P(n)->P(n)^2] FORMULAE
#Triplets[P(3)->P(3)^2] = 3; #Triplets_Corrected[P(3)->P(3)^2] = 3; actual number triplets in this interval = 4
#Triplets[P(4)->P(4)^2] = 4; #Triplets_Corrected[P(4)->P(4)^2] = 4; actual number triplets in this interval = 5
#Triplets[P(5)->P(5)^2] = 4; #Triplets_Corrected[P(5)->P(5)^2] = 4; actual number triplets in this interval = 5
#Triplets[P(6)->P(6)^2] = 6; #Triplets_Corrected[P(6)->P(6)^2] = 6; actual number triplets in this interval = 6
#Triplets[P(7)->P(7)^2] = 6; #Triplets_Corrected[P(7)->P(7)^2] = 6; actual number triplets in this interval = 8
#Triplets[P(8)->P(8)^2] = 7; #Triplets_Corrected[P(8)->P(8)^2] = 7; actual number triplets in this interval = 8
#Triplets[P(9)->P(9)^2] = 10; #Triplets_Corrected[P(9)->P(9)^2] = 10; actual number triplets in this interval = 10
#Triplets[P(10)->P(10)^2] = 11; #Triplets_Corrected[P(10)->P(10)^2] = 11; actual number triplets in this interval = 12
#Triplets[P(11)->P(11)^2] = 14; #Triplets_Corrected[P(11)->P(11)^2] = 14; actual number triplets in this interval = 15
#Triplets[P(12)->P(12)^2] = 16; #Triplets_Corrected[P(12)->P(12)^2] = 16; actual number triplets in this interval = 19
#Triplets[P(13)->P(13)^2] = 16; #Triplets_Corrected[P(13)->P(13)^2] = 16; actual number triplets in this interval = 19
#Triplets[P(14)->P(14)^2] = 18; #Triplets_Corrected[P(14)->P(14)^2] = 18; actual number triplets in this interval = 21
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EXAMINING THE #Quadruplets[P(n)->P(n)^2] AND #Quadruplets_Corrected[P(n)->P(n)^2] FORMULAE
#Quadruplets[P(3)->P(3)^2] = 1; #Quadruplets_Corrected[P(3)->P(3)^2] = 1; actual number quadruplets in this interval = 2
#Quadruplets[P(4)->P(4)^2] = 2; #Quadruplets_Corrected[P(4)->P(4)^2] = 2; actual number quadruplets in this interval = 3
#Quadruplets[P(5)->P(5)^2] = 1; #Quadruplets_Corrected[P(5)->P(5)^2] = 1; actual number quadruplets in this interval = 2
#Quadruplets[P(6)->P(6)^2] = 2; #Quadruplets_Corrected[P(6)->P(6)^2] = 2; actual number quadruplets in this interval = 3
#Quadruplets[P(7)->P(7)^2] = 2; #Quadruplets_Corrected[P(7)->P(7)^2] = 2; actual number quadruplets in this interval = 2
#Quadruplets[P(8)->P(8)^2] = 2; #Quadruplets_Corrected[P(8)->P(8)^2] = 2; actual number quadruplets in this interval = 2
#Quadruplets[P(9)->P(9)^2] = 3; #Quadruplets_Corrected[P(9)->P(9)^2] = 3; actual number quadruplets in this interval = 3
#Quadruplets[P(10)->P(10)^2] = 3; #Quadruplets_Corrected[P(10)->P(10)^2] = 3; actual number quadruplets in this interval = 3
#Quadruplets[P(11)->P(11)^2] = 3; #Quadruplets_Corrected[P(11)->P(11)^2] = 3; actual number quadruplets in this interval = 3
#Quadruplets[P(12)->P(12)^2] = 3; #Quadruplets_Corrected[P(12)->P(12)^2] = 3; actual number quadruplets in this interval = 4
#Quadruplets[P(13)->P(13)^2] = 3; #Quadruplets_Corrected[P(13)->P(13)^2] = 3; actual number quadruplets in this interval = 4
#Quadruplets[P(14)->P(14)^2] = 4; #Quadruplets_Corrected[P(14)->P(14)^2] = 4; actual number quadruplets in this interval = 6
Execution Time = 33seconds.