Inhaltsverzeichnis

Development of
Algorithmic Constructions
01:38:34
Deutsch
20.Apr 2024

Primes on quadric irreducible polynomials

The polynomials which are listed should fulfill the following conditions:
  1. The quadratic polynomials should be of the form f(x)=ax^2+bx+c, where a, b and c are elements of Z.
  2. The sequences start with x=0 and |f(0)|=|c| should be a prime number or equal 1.
  3. The polynomial should be irreducible, that means it should not be written as f(x)=(x+n)*(x+m), where n and m are integers.
  4. Every polynomial constructs a special sequence of primes which is infinite.
  5. The primes of the sequence are sorted in the list below.
  6. There are 178 different sequences.

Sort order

  1. I started the search for the polynoms from a=1 to a=4.
    For each value of a i made a loop of c=1, -1, 2, -2, 3, -3, 5, -5 up to 100, -100.
    For each value of a and b i made a loop for b from b=0, 1, -1, 2, -2, 3, -3, up to 300, -300.
    I only choose sequences with b=0 mod a because of the special mathematical proof.
    The first appearance of a sequence was choosen, all sequences were sorted and by that proceeding the table was created.
  2. |c| indicates the category. The primes p with p=f(x) are marked with green color.
  3. The prime sequences are sorted by arising primes.
You will find a better explanation of the algorithm, a mathematical proof and the distribution of the primes by following the link of the polynomial.

Results

Sequences
started with a=1
f(0)=239
f(0)=314
f(0)=58
f(0)=76
f(0)=113
f(0)=132
f(0)=17
f(0)=191
f(0)=23
f(0)=29
All73
Sequences
started with a=2
f(0)=2
f(0)=329
f(0)=513
f(0)=74
f(0)=116
f(0)=132
f(0)=171
f(0)=191
f(0)=23
f(0)=291
All57
Sequences
started with a=3
f(0)=226
f(0)=3
f(0)=54
f(0)=75
f(0)=112
f(0)=132
f(0)=171
f(0)=19
f(0)=23
f(0)=29
All40
Sequences
started with a=4
f(0)=2
f(0)=35
f(0)=51
f(0)=71
f(0)=11
f(0)=131
f(0)=17
f(0)=19
f(0)=23
f(0)=29
All8

Irreducible quadratic polynomials of the form ax^2+bx+c

x^2+bx+c Sequence start with 2

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./1./1. f(x)=x^2+4x-2f(x+2)=x^2-6242 3 5 19 23 29 43 47 53 67 71 73 97
2./2./2. f(x)=x^2+45x+2f(x+22.5)=x^2-504.252017 0.655202 3 7 11 23 29 31 41 61 71 73 79 83
3./3./3. f(x)=x^2-6x+2f(x-3)=x^2-7282 3 7 19 29 31 37 47 53 59 83
4./4./4. f(x)=x^2+21x+2f(x+10.5)=x^2-108.25433 0.665502 3 11 13 17 37 41 53 59 79
5./5./5. f(x)=x^2-2x-2f(x-1)=x^2-3122 3 11 13 23 37 47 59 61 71 73 83 97
6./6./6. f(x)=x^2+2f(x+0)=x^2+2-82 3 11 17 19 41 43 59 67 73 83 89 97
7./7./7. f(x)=x^2-51x+2f(x-25.5)=x^2-648.252593 0.663642 3 17 19 31 37 41 43 47 53 67 71 73 79
8./8./8. f(x)=x^2+47x-2f(x+23.5)=x^2-554.252217 0.682562 3 23 29 31 37 43 47 53 67 71 73 79 83 89
9./9./9. f(x)=x^2+95x-2f(x+47.5)=x^2-2258.259033 0.709942 3 47 61 67 71 73 83 89 97
10./10./10. f(x)=x^2-8x+2f(x-4)=x^2-14562 5 7 11 13 31 43 47 61 67
11./11./11. f(x)=x^2+6x-2f(x+3)=x^2-11442 5 7 11 19 37 43 53 79 83 89 97
12./12./12. f(x)=x^2+21x-2f(x+10.5)=x^2-112.25449 0.668972 5 7 11 23 41 53 59 61 67 89 97
13./13./13. f(x)=x^2+23x+2f(x+11.5)=x^2-130.25521 0.671522 5 11 13 29 31 37 47 53 59 71 83 97
14./14./14. f(x)=x^2-2x+2f(x-1)=x^2+1-42 5 13 17 29 37 41 53 61 73 89 97
15./15./15. f(x)=x^2-81x-2f(x-40.5)=x^2-1642.256569 0.674052 5 13 31 41 47 59 61 71 73 83 89 97
16./16./16. f(x)=x^2+103x+2f(x+51.5)=x^2-2650.2510601 0.684522 5 29 41 43 53 61 67 73 89
17./17./17. f(x)=x^2-163x+2f(x-81.5)=x^2-6640.2526561 0.698712 5 31 47 67 83 89
18./18./18. f(x)=x^2-10x+2f(x-5)=x^2-23922 7 11 13 19 23 29 41 43 67 73 79 83
19./19./19. f(x)=x^2+25x+2f(x+12.5)=x^2-154.25617 0.675692 7 11 19 31 37 41 43 47 59 67 71 79 83 97
20./20./20. f(x)=x^2-57x-2f(x-28.5)=x^2-814.253257 0.674082 7 11 29 31 37 41 47 53 59 79 89
21./21./21. f(x)=x^2+31x+2f(x+15.5)=x^2-238.25953 0.675242 7 13 17 29 37 41 53 59 67 71 73 79 83
22./22./22. f(x)=x^2+4x+2f(x+2)=x^2-282 7 17 23 31 41 47 71 73 79 89 97
23./23./23. f(x)=x^2+147x-2f(x+73.5)=x^2-5404.2521617 0.691572 7 31 37 41 43 53 73 79 83 89
24./24./24. f(x)=x^2+12x-2f(x+6)=x^2-38152 0.700292 11 13 17 19 29 31 37 43 53 71 73 79 83
25./25./25. f(x)=x^2-14x+2f(x-7)=x^2-47188 0.701962 11 17 19 23 31 37 43 47 53 61 67 89 97
26./26./26. f(x)=x^2+65x+2f(x+32.5)=x^2-1054.254217 0.683192 11 17 23 31 37 47 59 89
27./27./27. f(x)=x^2-177x-2f(x-88.5)=x^2-7834.2531337 0.718032 11 19 89 97
28./28./28. f(x)=x^2-91x+2f(x-45.5)=x^2-2068.258273 0.694602 11 23 41 43 47 71 73 89
29./29./29. f(x)=x^2+87x-2f(x+43.5)=x^2-1894.257577 0.701372 11 41 43 59 61 67 79 97
30./30./30. f(x)=x^2+49x+2f(x+24.5)=x^2-598.252393 0.686432 13 17 23 37 61 71 73 79 83 89 97
31./31./31. f(x)=x^2-16x+2f(x-8)=x^2-622482 13 19 23 29 31 37 41 53 59 61 67 79 97
32./32./32. f(x)=x^2+18x-2f(x+9)=x^2-83332 0.710142 17 19 29 37 41 43 47 61 67 71 79 83
33./33./33. f(x)=x^2+33x-2f(x+16.5)=x^2-274.251097 0.689182 17 23 29 41 47 53 59 61 67 71 73
34./34./34. f(x)=x^2+135x-2f(x+67.5)=x^2-4558.2518233 0.714852 17 31 43 53 67 71 97
35./35./35. f(x)=x^2+117x-2f(x+58.5)=x^2-3424.2513697 0.698942 19 23 29 37 43 59 67 73 89
36./36./36. f(x)=x^2+35x+2f(x+17.5)=x^2-304.251217 0.691222 19 29 31 37 43 47 61 71 73 79 97
37./37./37. f(x)=x^2-26x+2f(x-13)=x^2-167668 0.725402 23 29 43 59 61 67 71 79 83 89 97
38./38./38. f(x)=x^2+30x-2f(x+15)=x^2-227908 0.734902 29 31 53 67 73 83 89 97
39./39./39. f(x)=x^2-40x+2f(x-20)=x^2-3981592 0.757132 37 43 71 89

x^2+bx+c Sequence start with 3

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./40./40. f(x)=x^2+43x-3f(x+21.5)=x^2-465.2518613 5 17 29 31 37 41 47 53 71 73 79 89 97
2./41./41. f(x)=x^2+133x-3f(x+66.5)=x^2-4425.25177013 5 17 31 53 59 73 79 89 97
3./42./42. f(x)=x^2+41x+3f(x+20.5)=x^2-417.251669 0.680243 5 19 23 29 37 43 47 59 61 71 79 83 89
4./43./43. f(x)=x^2-3x+3f(x-1.5)=x^2+0.75-33 7 13 19 31 37 43 61 67 73 79 97
5./44./44. f(x)=x^2-25x+3f(x-12.5)=x^2-153.256133 7 17 19 29 37 41 43 47 61 67 71 89 97
6./45./45. f(x)=x^2-95x-3f(x-47.5)=x^2-2259.2590373 7 31 37 61 67 71 79 97
7./46./46. f(x)=x^2-65x+3f(x-32.5)=x^2-1053.2542133 11 13 23 31 41 61 67 71 79 83
8./47./47. f(x)=x^2+35x-3f(x+17.5)=x^2-309.251237 0.689863 11 17 23 31 37 59 71 73 79 83 89 97
9./48./48. f(x)=x^2+55x-3f(x+27.5)=x^2-759.2530373 11 19 23 37 53 59 61 67 83 89
10./49./49. f(x)=x^2+103x+3f(x+51.5)=x^2-2649.25105973 11 59 71 73 79 97
11./50./50. f(x)=x^2+41x-3f(x+20.5)=x^2-423.251693 0.698253 13 31 37 43 47 59 61 71 83 89 97
12./51./51. f(x)=x^2+29x-3f(x+14.5)=x^2-213.25853 0.696683 19 23 31 41 43 47 59 61 67 71 73 83
13./52./52. f(x)=x^2+125x-3f(x+62.5)=x^2-3909.2515637 0.736923 19 29 41 67 83
14./53./53. f(x)=x^2+85x+3f(x+42.5)=x^2-1803.2572133 59 61 83 89 97

x^2+bx+c Sequence start with 5

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./54./54. f(x)=x^2+23x+5f(x+11.5)=x^2-127.25509 0.697215 11 17 23 29 37 43 67 71 73 83 89 97
2./55./55. f(x)=x^2-5x+5f(x-2.5)=x^2-1.2555 11 19 29 31 41 59 61 71 79 89
3./56./56. f(x)=x^2+51x-5f(x+25.5)=x^2-655.2526215 11 43 47 53 59 83 89 97
4./57./57. f(x)=x^2+21x-5f(x+10.5)=x^2-115.254615 17 19 23 41 43 53 59 61 67 73 89 97
5./58./58. f(x)=x^2+53x+5f(x+26.5)=x^2-697.252789 0.708675 17 23 29 41 47 59 71 97
6./59./59. f(x)=x^2+31x+5f(x+15.5)=x^2-235.259415 29 37 41 43 47 53 71 73 79 83
7./60./60. f(x)=x^2+63x-5f(x+31.5)=x^2-997.253989 0.732475 29 37 59 67 89 97
8./61./61. f(x)=x^2+73x+5f(x+36.5)=x^2-1327.255309 0.737825 31 41 53 67 79

x^2+bx+c Sequence start with 7

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./62./62. f(x)=x^2+25x-7f(x+12.5)=x^2-163.25653 0.697087 11 13 19 23 31 47 53 59 73 79
2./63./63. f(x)=x^2+23x-7f(x+11.5)=x^2-139.25557 0.708527 17 19 29 43 59 67 71 73 79 83 97
3./64./64. f(x)=x^2-45x+7f(x-22.5)=x^2-499.251997 0.717527 17 29 37 53 61 67 71 79 89
4./65./65. f(x)=x^2+39x+7f(x+19.5)=x^2-373.251493 0.718237 19 31 43 47 53 67 71 89
5./66./66. f(x)=x^2-65x-7f(x-32.5)=x^2-1063.2542537 19 53 59 71 73
6./67./67. f(x)=x^2+43x-7f(x+21.5)=x^2-469.2518777 37 41 59 61 67 83 89

x^2+bx+c Sequence start with 11

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./68./68. f(x)=x^2+29x+11f(x+14.5)=x^2-199.25797 0.7131311 13 17 41 43 61 67 71 73 89
2./69./69. f(x)=x^2+41x+11f(x+20.5)=x^2-409.251637 0.7117011 13 23 29 31 37 53 67 71 97
3./70./70. f(x)=x^2+27x-11f(x+13.5)=x^2-193.25773 0.7238311 17 37 47 61 67 79 83 97

x^2+bx+c Sequence start with 13

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./71./71. f(x)=x^2+59x-13f(x+29.5)=x^2-883.253533 0.7546313 29 47 61 67 71
2./72./72. f(x)=x^2+27x+13f(x+13.5)=x^2-169.25677 0.7349113 37 41 59 71 79 97

x^2+bx+c Sequence start with 19

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./73./73. f(x)=x^2+49x-19f(x+24.5)=x^2-619.252477 0.7531519 23 31 67 83

2x^2+bx+c Sequence start with 3

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./1./74. f(x)=2x^2+16x-3f(x+4)=2*x^2-35280 0.702963 5 7 11 17 23 31 37 53 61 73 83 97
2./2./75. f(x)=2x^2-28x+3f(x-7)=2*x^2-95760 0.696323 5 7 11 19 23 29 31 47 67 71 79 97
3./3./76. f(x)=2x^2+3f(x+0)=2*x^2+3-24 0.707293 5 7 11 29 31 53 59 73 79 83 97
4./4./77. f(x)=2x^2-12x+3f(x-3)=2*x^2-15120 0.713093 5 7 13 17 19 29 37 71 83
5./5./78. f(x)=2x^2+64x-3f(x+16)=2*x^2-5154120 0.690903 5 7 13 19 23 31 41 43 59 67 71 73
6./6./79. f(x)=2x^2-20x-3f(x-5)=2*x^2-53424 0.696743 5 7 17 19 47 53 61 67 83 89 97
7./7./80. f(x)=2x^2-50x+3f(x-12.5)=2*x^2-309.52476 0.694183 5 11 19 37 41 43 47 53 59 61 67 73 83 89
8./8./81. f(x)=2x^2-20x+3f(x-5)=2*x^2-47376 0.700153 5 13 17 23 29 31 47 59 83 89 97
9./9./82. f(x)=2x^2-70x-3f(x-17.5)=2*x^2-615.54924 0.694613 5 13 23 29 37 41 47 59 67 71 79 83
10./10./83. f(x)=2x^2+8x+3f(x+2)=2*x^2-540 0.716553 5 13 31 37 41 43 53 67 71 79 83 89
11./11./84. f(x)=2x^2-52x+3f(x-13)=2*x^2-3352680 0.706033 5 19 23 31 37 43 47 59 61 67 79 89 97
12./12./85. f(x)=2x^2+12x-3f(x+3)=2*x^2-21168 0.715303 7 11 13 17 19 29 41 47 53 61 79 89
13./13./86. f(x)=2x^2+16x+3f(x+4)=2*x^2-29232 0.705013 7 11 19 23 29 37 43 61 71
14./14./87. f(x)=2x^2-62x-3f(x-15.5)=2*x^2-483.53868 0.699563 7 17 19 23 43 47 53 61 67 73 79 97
15./15./88. f(x)=2x^2-68x-3f(x-17)=2*x^2-5814648 0.716253 7 23 43 47 53 59 61 67 73 83 89 97
16./16./89. f(x)=2x^2+52x-3f(x+13)=2*x^2-3412728 0.709983 11 17 19 31 37 47 53 71 73 79 97
17./17./90. f(x)=2x^2+28x-3f(x+7)=2*x^2-101808 0.706483 11 17 23 29 31 47 53 59 61 67 71 79 83 97
18./18./91. f(x)=2x^2-106x+3f(x-26.5)=2*x^2-1401.511212 0.715343 11 17 37 53 61 67 79 83 89
19./19./92. f(x)=2x^2-104x+3f(x-26)=2*x^2-134910792 0.712333 11 19 29 31 37 41 61 71 73 97
20./20./93. f(x)=2x^2+32x-3f(x+8)=2*x^2-1311048 0.707893 11 23 29 31 37 41 43 47 59 71 79 89
21./21./94. f(x)=2x^2-64x+3f(x-16)=2*x^2-5094072 0.706703 13 17 19 23 53 59 61 71 73 89 97
22./22./95. f(x)=2x^2+46x+3f(x+11.5)=2*x^2-261.52092 0.709763 13 17 29 41 47 53 59 67 73 79 83 89
23./23./96. f(x)=2x^2+112x-3f(x+28)=2*x^2-157112568 0.719113 13 19 37 53 59 67 71 73
24./24./97. f(x)=2x^2-24x+3f(x-6)=2*x^2-69552 0.724283 17 19 23 29 31 37 43 59 61 67 73 89
25./25./98. f(x)=2x^2-158x-3f(x-39.5)=2*x^2-3123.524988 0.740243 17 31 53 61 67 89
26./26./99. f(x)=2x^2+172x-3f(x+43)=2*x^2-370129608 0.740773 19 29 43 59 71 79
27./27./100. f(x)=2x^2-76x+3f(x-19)=2*x^2-7195752 0.731903 23 47 53 59 71 79 83
28./28./101. f(x)=2x^2-36x+3f(x-9)=2*x^2-1591272 0.740623 29 31 41 43 47 53 61 79 83 97
29./29./102. f(x)=2x^2+134x+3f(x+33.5)=2*x^2-2241.517932 0.753653 31 43 47 71 83

2x^2+bx+c Sequence start with 5

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./30./103. f(x)=2x^2+5f(x+0)=2*x^2+5-40 0.711245 7 11 13 19 23 37 41 47 53 59 89
2./31./104. f(x)=2x^2-24x+5f(x-6)=2*x^2-67536 0.707985 7 13 17 19 31 53 59 61 67 73 79 83 89
3./32./105. f(x)=2x^2+16x-5f(x+4)=2*x^2-37296 0.711085 7 13 19 29 37 41 43 47 59 61 71 73
4./33./106. f(x)=2x^2-32x-5f(x-8)=2*x^2-1331064 0.715505 7 19 23 29 31 37 41 53 61 67 83 89 97
5./34./107. f(x)=2x^2-42x+5f(x-10.5)=2*x^2-215.51724 0.712865 7 29 31 41 43 47 53 61 67 71 79 83 97
6./35./108. f(x)=2x^2+12x+5f(x+3)=2*x^2-13104 0.717845 11 13 17 19 23 37 59 67 79 83
7./36./109. f(x)=2x^2-54x+5f(x-13.5)=2*x^2-359.52876 0.706895 11 13 19 23 29 37 43 47 61 67 71 79
8./37./110. f(x)=2x^2+20x-5f(x+5)=2*x^2-55440 0.724665 11 17 23 29 37 43 47 53 59 61 73 79 83 89
9./38./111. f(x)=2x^2+64x-5f(x+16)=2*x^2-5174136 0.735705 11 41 47 61 67 71 73 83 89 97
10./39./112. f(x)=2x^2+56x-5f(x+14)=2*x^2-3973176 0.721545 13 23 31 47 53 59 61 73 79 97
11./40./113. f(x)=2x^2+72x+5f(x+18)=2*x^2-6435144 0.731165 13 37 47 61 71 79 83 89 97
12./41./114. f(x)=2x^2-28x-5f(x-7)=2*x^2-103824 0.719025 17 19 31 37 41 47 53 59 71 83 97
13./42./115. f(x)=2x^2+36x+5f(x+9)=2*x^2-1571256 0.722195 17 29 31 43 47 53 59 61 71 83 89

2x^2+bx+c Sequence start with 7

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./43./116. f(x)=2x^2-24x-7f(x-6)=2*x^2-79632 0.720417 11 19 29 37 47 53 61 67 71 73 79 83 89 97
2./44./117. f(x)=2x^2-28x+7f(x-7)=2*x^2-91728 0.733427 13 19 37 41 43 59 61 71 73 83 89 97
3./45./118. f(x)=2x^2-54x-7f(x-13.5)=2*x^2-371.52972 0.746477 37 41 53 59 67 79 97
4./46./119. f(x)=2x^2+58x+7f(x+14.5)=2*x^2-413.53308 0.750087 43 47 59 61 67 73

2x^2+bx+c Sequence start with 11

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./47./120. f(x)=2x^2-52x-11f(x-13)=2*x^2-3492792 0.7226011 13 17 23 31 41 43 53 59 61 73
2./48./121. f(x)=2x^2+11f(x+0)=2*x^2+11-88 0.7243911 13 19 23 29 31 43 47 61 71 83 89 97
3./49./122. f(x)=2x^2-38x-11f(x-9.5)=2*x^2-191.51532 0.7395111 17 29 47 59 73 79 83
4./50./123. f(x)=2x^2-92x-11f(x-23)=2*x^2-10698552 0.7563311 17 43 61 71 79 83 89 97
5./51./124. f(x)=2x^2+24x+11f(x+6)=2*x^2-61488 0.7354211 29 37 41 43 47 53 59 61 67 73 97
6./52./125. f(x)=2x^2-62x-11f(x-15.5)=2*x^2-491.53932 0.7623111 37 41 53 71 83 89

2x^2+bx+c Sequence start with 13

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./53./126. f(x)=2x^2+44x+13f(x+11)=2*x^2-2291832 0.7446313 17 29 59 67 71 97
2./54./127. f(x)=2x^2-46x+13f(x-11.5)=2*x^2-251.52012 0.7479113 19 31 61 71 73 97

2x^2+bx+c Sequence start with 17

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./55./128. f(x)=2x^2-78x+17f(x-19.5)=2*x^2-743.55948 0.7597717 19 37 43 59 73 79 97

2x^2+bx+c Sequence start with 19

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./56./129. f(x)=2x^2+40x+19f(x+10)=2*x^2-1811448 0.7666019 53 61 73 79 83

2x^2+bx+c Sequence start with 29

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./57./130. f(x)=2x^2+29f(x+0)=2*x^2+29-232 0.7581329 31 37 47 59 61 67 79 83

3x^2+bx+c Sequence start with 2

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./1./131. f(x)=3x^2-6x-2f(x-1)=3*x^2-5602 5 7 11 17 43 53 59 61 67 71
2./2./132. f(x)=3x^2+111x-2f(x+18.5)=3*x^2-1028.7512345 0.694662 5 7 11 29 31 41 43 53 67 73 79 83
3./3./133. f(x)=3x^2+2f(x+0)=3*x^2+2-24 0.717522 5 7 11 29 31 53 59 73 79 83 97
4./4./134. f(x)=3x^2-12x+2f(x-2)=3*x^2-10120 0.723272 5 7 13 17 19 29 37 71 83
5./5./135. f(x)=3x^2+75x+2f(x+12.5)=3*x^2-466.755601 0.690532 5 7 17 23 29 41 43 47 53 67 83 97
6./6./136. f(x)=3x^2-45x-2f(x-7.5)=3*x^2-170.752049 0.696392 5 11 17 19 23 41 47 61 67 89 97
7./7./137. f(x)=3x^2-2f(x+0)=3*x^2-2242 5 19 23 29 43 47 53 67 71 73 97
8./8./138. f(x)=3x^2-81x-2f(x-13.5)=3*x^2-548.756585 0.713922 5 19 37 41 43 53 59 61 67 83 89 97
9./9./139. f(x)=3x^2-87x+2f(x-14.5)=3*x^2-628.757545 0.714602 5 23 29 37 41 47 61 71 79 83 89
10./10./140. f(x)=3x^2-12x-2f(x-2)=3*x^2-14168 0.725442 7 11 13 17 19 29 41 47 53 61 79 89
11./11./141. f(x)=3x^2-51x+2f(x-8.5)=3*x^2-214.752577 0.698392 7 11 13 23 29 31 43 61 79 83 89
12./12./142. f(x)=3x^2-57x-2f(x-9.5)=3*x^2-272.753273 0.699462 7 13 17 19 29 31 53 59 73 83 89 97
13./13./143. f(x)=3x^2+117x-2f(x+19.5)=3*x^2-1142.7513713 0.729432 7 29 47 59 61 71 79 97
14./14./144. f(x)=3x^2+87x-2f(x+14.5)=3*x^2-632.757593 0.706942 11 13 23 29 41 43 59 67 73 79 83 97
15./15./145. f(x)=3x^2-6x+2f(x-1)=3*x^2-1122 11 13 23 37 47 59 61 71 73 83 97
16./16./146. f(x)=3x^2-81x+2f(x-13.5)=3*x^2-544.756537 0.708752 11 17 19 37 41 43 47 71 83 89
17./17./147. f(x)=3x^2+39x+2f(x+6.5)=3*x^2-124.751497 0.709492 11 17 23 31 41 43 53 59 67 71 73 83 89
18./18./148. f(x)=3x^2-18x-2f(x-3)=3*x^2-29348 0.729592 13 17 19 23 29 31 41 43 59 71 79 83 89
19./19./149. f(x)=3x^2-111x+2f(x-18.5)=3*x^2-1024.7512297 0.718702 13 19 29 53 59 61 67 79 97
20./20./150. f(x)=3x^2+213x-2f(x+35.5)=3*x^2-3782.7545393 0.737372 13 31 53 59 61 71 83 97
21./21./151. f(x)=3x^2-24x+2f(x-4)=3*x^2-46552 0.734342 17 19 23 29 31 37 43 59 61 67 73 89
22./22./152. f(x)=3x^2-141x+2f(x-23.5)=3*x^2-1654.7519857 0.731302 17 23 37 67 71 73 89
23./23./153. f(x)=3x^2+69x+2f(x+11.5)=3*x^2-394.754737 0.723472 19 31 37 47 59 67 73 79 89 97
24./24./154. f(x)=3x^2-36x+2f(x-6)=3*x^2-1061272 0.750522 29 31 41 43 47 53 61 79 83 97
25./25./155. f(x)=3x^2-123x-2f(x-20.5)=3*x^2-1262.7515153 0.747732 31 43 59 61 71 79
26./26./156. f(x)=3x^2-42x-2f(x-7)=3*x^2-1491788 0.760372 37 41 43 47 61 73 79 89

3x^2+bx+c Sequence start with 5

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./27./157. f(x)=3x^2-69x-5f(x-11.5)=3*x^2-401.754821 0.730505 11 29 31 37 47 67 71 73 79 83
2./28./158. f(x)=3x^2-57x-5f(x-9.5)=3*x^2-275.753309 0.733555 11 37 43 59 61 67 71 73 89 97
3./29./159. f(x)=3x^2-123x+5f(x-20.5)=3*x^2-1255.7515069 0.763765 23 37 53
4./30./160. f(x)=3x^2-111x-5f(x-18.5)=3*x^2-1031.7512381 0.770925 41 43 71 89 97

3x^2+bx+c Sequence start with 7

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./31./161. f(x)=3x^2-69x+7f(x-11.5)=3*x^2-389.754677 0.731297 13 17 23 47 53 59 61 67 79 83 89
2./32./162. f(x)=3x^2+9x+7f(x+1.5)=3*x^2+0.25-37 13 19 31 37 43 61 67 73 79 97
3./33./163. f(x)=3x^2-87x-7f(x-14.5)=3*x^2-637.757653 0.756617 13 67 73 83 89
4./34./164. f(x)=3x^2-39x+7f(x-6.5)=3*x^2-119.751437 0.738397 17 29 41 47 53 59 61 73 83 97
5./35./165. f(x)=3x^2-129x+7f(x-21.5)=3*x^2-1379.7516557 0.779007 17 79 83

3x^2+bx+c Sequence start with 11

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./36./166. f(x)=3x^2-75x+11f(x-12.5)=3*x^2-457.755493 0.7606411 17 41 61 73 79 89 97
2./37./167. f(x)=3x^2-45x+11f(x-7.5)=3*x^2-157.751893 0.7578711 31 43 53 59 67 79 97

3x^2+bx+c Sequence start with 13

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./38./168. f(x)=3x^2-57x+13f(x-9.5)=3*x^2-257.753093 0.7566313 17 41 43 59 71 73 89 97
2./39./169. f(x)=3x^2-51x-13f(x-8.5)=3*x^2-229.752757 0.7713713 41 53 61 67 89

3x^2+bx+c Sequence start with 17

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./40./170. f(x)=3x^2-33x-17f(x-5.5)=3*x^2-107.751293 0.7578717 19 47 61 71 83 89 97

4x^2+bx+c Sequence start with 3

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./1./171. f(x)=4x^2+32x+3f(x+4)=4*x^2-619763 5 13 19 41 47 61 73 83 97
2./2./172. f(x)=4x^2-124x+3f(x-15.5)=4*x^2-95815328 0.721913 11 13 29 31 37 47 53 73 79 89 97
3./3./173. f(x)=4x^2-24x+3f(x-3)=4*x^2-33528 0.755403 11 17 29 31 37 41 67 83 97
4./4./174. f(x)=4x^2-40x+3f(x-5)=4*x^2-971552 0.742713 11 31 43 47 53 61 73 79 89 97
5./5./175. f(x)=4x^2+16x+3f(x+2)=4*x^2-132083 13 17 23 29 43 53 61 79

4x^2+bx+c Sequence start with 5

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./6./176. f(x)=4x^2-24x-5f(x-3)=4*x^2-416565 23 31 37 41 43 59 61 73 83

4x^2+bx+c Sequence start with 7

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./7./177. f(x)=4x^2+7f(x+0)=4*x^2+7-1127 11 23 29 37 43 53 67 71 79

4x^2+bx+c Sequence start with 13

PolynomPolynomb^2-4acPrimedensity2357111317192329313741434753596167717379838997
1./8./178. f(x)=4x^2-8x-13f(x-1)=4*x^2-1727213 17 19 43 47 53 59 67 83 89