## T3 Sequence

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• The following is a program written in BASIC: It doesn t use trial factoring, or exponentiation; It uses what the author describes as a T3 sequence. just cut
Message 1 of 1 , Jan 30, 2008
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The following is a program written in BASIC:
It doesn't use trial factoring, or exponentiation;
It uses what the author describes as a T3 sequence.
just cut and paste it... and run it...
It works in polynomial time and is deterministic.
The results are fool proof... and I can discuss it with anyone.

38 CLS
40 INPUT N
42 DIM A(100)
44 A(0) = N: A(1) = (N + 1) / 2: A(2) = A(1) - 1
46 FOR I = 0 TO 2: PRINT I, A(I): NEXT I
48 FOR J = 3 TO 100 STEP 2
50 IF A(J - 1) <= 2 THEN
52 IF A(J - 1) = 2 THEN
54 A(J) = 1: PRINT J, A(J): A(J + 1) = 0:
56 PRINT J + 1, A(J + 1): M = J + 1: J = 100
58 ELSE
60 A(J) = 0: PRINT J, A(J): M = J: J = 100
62 END IF
64 ELSE
66 IF A(J - 1) MOD 2 = 1 THEN
68 A(J) = A(J - 2) / 2
70 ELSE
72 A(J) = (A(J - 2) + 1) / 2
74 END IF
76 A(J + 1) = A(J) - 1: PRINT J, A(J): PRINT J + 1, A(J + 1)
78 END IF
80 NEXT J
82 PRINT
84 DIM T(3)
86 T(0) = 2: T(1) = 3: T(2) = (T(1) ^ 2 - 2) MOD N
88 IF T(2) = 0 THEN T(2) = T(2) + N
90 FOR I = 0 TO 2: PRINT M - I, I, T(I): NEXT I
100 K = 0
102 FOR L = M - 3 TO 0 STEP -1
104 IF A(L) MOD 2 = 1 THEN
106 IF A(L) = A(L + 1) + A(L + 2) THEN K = 0 ELSE K = 1
108 T(3) = (T(2 - K) * T(1 - K) - 3) MOD N
110 ELSE
112 T(3) = (T(1) ^ 2 - 2) MOD N
114 END IF
116 IF T(3) = 0 THEN T(3) = T(3) + N
117 PRINT L, A(L), T(3)
118 Z = T(2) MOD 2
119 T(0) = T(1): T(1) = T(2): T(2) = T(3)
120 NEXT L
122 IF Z = 1 AND T(3) = 3 THEN
124 PRINT "The number", N, " is prime."
126 ELSE
128 PRINT "The number", N, " is composite."
130 END IF
132 SLEEP 5: GOTO 38

Bill B.
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