Inhaltsverzeichnis

Development of
Algorithmic Constructions

16:10:25
Deutsch
28.Mar 2024

Polynom = x^2-124x-613

0. Sequence

1. Algorithm

2. Mathematical background

3. Correctness of the algorithm

4. Infinity of the sequence

5. Sequence of the polynom with 1

6. Sequence of the polynom (only primes)

7. Distribution of the primes

8. Check for existing Integer Sequences by OEIS

0. Sequence

f(0) = 613 = 613
f(1) = 23 = 23
f(2) = 857 = 857
f(3) = 61 = 61
f(4) = 1093 = 1093
f(5) = 151 = 151
f(6) = 1321 = 1321
f(7) = 179 = 179
f(8) = 1541 = 23*67
f(9) = 103 = 103
f(10) = 1753 = 1753
f(11) = 29 = 29
f(12) = 1957 = 19*103
f(13) = 257 = 257
f(14) = 2153 = 2153
f(15) = 281 = 281
f(16) = 2341 = 2341
f(17) = 19 = 19
f(18) = 2521 = 2521
f(19) = 163 = 163
f(20) = 2693 = 2693
f(21) = 347 = 347
f(22) = 2857 = 2857
f(23) = 367 = 367
f(24) = 3013 = 23*131
f(25) = 193 = 193
f(26) = 3161 = 29*109
f(27) = 101 = 101
f(28) = 3301 = 3301
f(29) = 421 = 421
f(30) = 3433 = 3433
f(31) = 437 = 19*23
f(32) = 3557 = 3557
f(33) = 113 = 113
f(34) = 3673 = 3673
f(35) = 233 = 233
f(36) = 3781 = 19*199
f(37) = 479 = 479
f(38) = 3881 = 3881
f(39) = 491 = 491
f(40) = 3973 = 29*137
f(41) = 251 = 251
f(42) = 4057 = 4057
f(43) = 1 = 1
f(44) = 4133 = 4133
f(45) = 521 = 521
f(46) = 4201 = 4201
f(47) = 529 = 23*23
f(48) = 4261 = 4261
f(49) = 67 = 67
f(50) = 4313 = 19*227
f(51) = 271 = 271
f(52) = 4357 = 4357
f(53) = 547 = 547
f(54) = 4393 = 23*191
f(55) = 551 = 19*29
f(56) = 4421 = 4421
f(57) = 277 = 277
f(58) = 4441 = 4441
f(59) = 139 = 139
f(60) = 4453 = 61*73
f(61) = 557 = 557
f(62) = 4457 = 4457
f(63) = 557 = 557
f(64) = 4453 = 61*73
f(65) = 139 = 139
f(66) = 4441 = 4441
f(67) = 277 = 277
f(68) = 4421 = 4421
f(69) = 551 = 19*29
f(70) = 4393 = 23*191
f(71) = 547 = 547
f(72) = 4357 = 4357
f(73) = 271 = 271
f(74) = 4313 = 19*227
f(75) = 67 = 67
f(76) = 4261 = 4261
f(77) = 529 = 23*23
f(78) = 4201 = 4201
f(79) = 521 = 521
f(80) = 4133 = 4133
f(81) = 1 = 1
f(82) = 4057 = 4057
f(83) = 251 = 251
f(84) = 3973 = 29*137
f(85) = 491 = 491
f(86) = 3881 = 3881
f(87) = 479 = 479
f(88) = 3781 = 19*199
f(89) = 233 = 233
f(90) = 3673 = 3673
f(91) = 113 = 113
f(92) = 3557 = 3557
f(93) = 437 = 19*23
f(94) = 3433 = 3433
f(95) = 421 = 421
f(96) = 3301 = 3301
f(97) = 101 = 101
f(98) = 3161 = 29*109
f(99) = 193 = 193
f(100) = 3013 = 23*131

1. Algorithm

If you are interested in some better algorithms have a look at quadr_Sieb_x^2+1.php.

2. Mathematical background

Lemma: If p | f(x) then also p | f(x+p) and p | f(-x-b/a) a) p | f(x) <=> ax^2 + bx + c = 0 mod p p | f(x+p) <=> a(x+p)^2 + b(x+p) + c = 0 mod p <=> ax^2 + 2axp + ap^2 + bx + bp + c = 0 mod p <=> ax^2 + bx + c = 0 mod p Thus if p | f(x) then p | f(x+p) b) if b = 0 mod a p | f(x) <=> ax^2 + bx + c = 0 mod p p | f(-x-b/a) <=> a(-x-b/a)^2 + b(-x-b/a) + c = 0 mod p <=> ax^2 + 2bx + b^2/a - bx - b^2/a + c = 0 mod p <=> ax^2 + bx + c = 0 mod p Thus if p | f(x) then p | f(-x-b/a)

3. Correctness of the algorithm

The proof for this polynom is similar to the proof for the polynom f(x)=x^2-4x+1. a) First terms for the polynom f(x) = x^2-124x-613

f(0)=613
f(1)=23
f(2)=857
f(3)=61
f(4)=1093
f(5)=151
f(6)=1321
f(7)=179
f(8)=67
f(9)=103
f(10)=1753
f(11)=29
f(12)=19
f(13)=257
f(14)=2153
f(15)=281
f(16)=2341
f(17)=1
f(18)=2521
f(19)=163
f(20)=2693
f(21)=347
f(22)=2857
f(23)=367
f(24)=131
f(25)=193
f(26)=109
f(27)=101
f(28)=3301
f(29)=421
f(30)=3433
f(31)=1
f(32)=3557
f(33)=113
f(34)=3673
f(35)=233
f(36)=199
f(37)=479
f(38)=3881
f(39)=491
f(40)=137
f(41)=251
f(42)=4057
f(43)=1
f(44)=4133
f(45)=521
f(46)=4201
f(47)=1
f(48)=4261
f(49)=1
f(50)=227
f(51)=271
f(52)=4357
f(53)=547
f(54)=191
f(55)=1
f(56)=4421
f(57)=277
f(58)=4441
f(59)=139
f(60)=73
f(61)=557
f(62)=4457
f(63)=1
f(64)=1
f(65)=1
f(66)=1
f(67)=1
f(68)=1
f(69)=1
f(70)=1
f(71)=1
f(72)=1
f(73)=1
f(74)=1
f(75)=1
f(76)=1
f(77)=1
f(78)=1
f(79)=1
f(80)=1
f(81)=1
f(82)=1
f(83)=1
f(84)=1
f(85)=1
f(86)=1
f(87)=1
f(88)=1
f(89)=1
f(90)=1
f(91)=1
f(92)=1
f(93)=1
f(94)=1
f(95)=1
f(96)=1
f(97)=1
f(98)=1
f(99)=1

b) Substitution of the polynom
The polynom f(x)=x^2-124x-613 could be written as f(y)= y^2-4457 with x=y+62

c) Backsubstitution Beside by backsubstitution you get an estimation for the huge of the primes with p | f(x) and p < f(x) f'(y)>(2y-1) with with y=x-62
f'(x)>2x-125 with x > 67

4. Infinity of the sequence

The mathematical proof is analogue to the proof for the polynom f(x)=x^2+1

5. Sequence of the polynom with 1

613, 23, 857, 61, 1093, 151, 1321, 179, 67, 103, 1753, 29, 19, 257, 2153, 281, 2341, 1, 2521, 163, 2693, 347, 2857, 367, 131, 193, 109, 101, 3301, 421, 3433, 1, 3557, 113, 3673, 233, 199, 479, 3881, 491, 137, 251, 4057, 1, 4133, 521, 4201, 1, 4261, 1, 227, 271, 4357, 547, 191, 1, 4421, 277, 4441, 139, 73, 557, 4457, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 167, 1, 443, 1, 727, 1, 1019, 1, 1319, 1, 1627, 223, 1, 263, 2267, 1, 1, 173, 2939, 389, 1, 433, 3643, 239, 4007, 1, 1, 571, 4759, 619, 5147, 1, 241, 359, 313, 769, 6359, 821, 6779, 1, 7207, 1, 7643, 983, 8087, 1039, 8539, 1, 8999, 577, 9467, 1213, 1, 1, 10427, 1, 1, 349, 601, 1459, 11927, 1523, 541, 397, 12967, 827, 13499, 1721, 1, 1789, 503, 929, 797, 1, 1, 1999, 1, 1, 733, 1, 1, 1109, 18043, 2293, 643, 1, 19259, 1223, 1, 631, 20507, 1, 21143, 2683, 21787, 691, 1181, 1423, 23099, 1, 23767, 1, 24443, 1549, 25127, 1, 25819, 3271, 1153, 3359, 1433, 431, 27943, 1, 1, 1, 29399, 1, 30139, 1907, 461, 977, 31643, 4003, 1409, 4099, 33179, 1049, 1171, 1, 34747, 1, 35543, 4493, 1913, 2297, 37159, 587, 1, 4799, 1, 4903, 1367, 1, 40487, 2557, 617, 1, 2221, 1, 43067, 2719, 43943, 1, 1949, 5659, 1, 1, 46619, 1471, 47527, 2999, 1, 6113, 49367, 6229, 1, 1, 51239, 1, 2269, 1, 2797, 6703, 887, 853, 55079, 1, 919, 7069, 57047, 7193, 58043, 3659, 1, 1861, 1, 1, 593, 7699, 1, 1, 1, 1, 64187, 8089, 65239, 8221, 1, 4177, 1, 1061, 68443, 8623, 1, 1, 70619, 1, 71719, 4517, 3833, 9173, 73943, 1, 1, 1, 3313, 2399, 77339, 9739, 78487, 9883, 1091, 1, 4253, 5087, 1123, 10321, 607, 1, 84347, 5309, 653, 673, 1, 1, 87959, 11071, 1, 1, 90407, 5689, 811, 1, 3203, 11689, 4093, 5923, 5021, 3001, 96667, 12163, 97943, 12323, 1481, 3121, 100519, 6323, 3511, 12809, 1, 12973, 1, 6569, 105767, 1663, 107099, 709, 108439, 1, 1087, 863, 111143, 1, 112507, 14149, 1, 14321, 115259, 7247, 1741, 1, 118043, 14843, 119447, 1, 6361, 1, 122279, 7687, 123707, 1, 5441, 15733, 1229, 1, 2099, 1, 129499, 1, 1, 1, 4567, 2081, 1, 1, 1, 17021, 5953, 17209, 138427, 8699, 139943, 4397, 1, 773, 4931, 17971, 144539, 1, 1, 1, 1, 18553, 7853, 18749, 150779, 9473, 1009, 2393, 153947, 1, 1427, 19543, 941, 1, 158759, 9973, 1, 20149, 162007, 20353, 163643, 1, 165287, 1, 1201, 1, 168599, 21179, 170267, 5347, 1237, 10799, 7549, 1, 881, 1, 177019, 11117, 6163, 1, 9497, 1, 182167, 1, 1063, 2887, 2543, 11657, 187387, 1, 2591, 23753, 1, 11987, 10141, 1, 1193, 24419, 196247, 1297, 198043, 6217, 8689, 12547, 1, 25321, 3037, 1, 205307, 12889, 1, 3251, 2029, 1381, 210839, 1, 937, 1669, 1, 13469, 2143, 1, 2003, 27409, 1, 1, 1, 6971, 224027, 28123, 225943, 1, 1, 7151, 229799, 14423, 1, 1531, 233687, 29333, 3863, 1, 237607, 1, 239579, 30071, 241559, 30319, 10589, 3821, 8467, 1, 247547, 31069, 1, 31321, 13241, 15787, 253607, 1, 1693, 32083, 257687, 1, 1, 1, 261799, 16427, 263867, 33113, 13997, 1451, 1, 1, 1, 1, 1987, 34159, 1, 1187, 276443, 1, 1709, 17477, 280699, 35221, 2503, 1543, 1, 1, 2843, 9007, 1499, 36299, 1, 36571, 293659, 1, 295847, 1, 298043, 1, 300247, 1, 302459, 18973, 1, 2389, 1, 1, 13441, 38783, 2377, 1, 313639, 1, 315899, 1723, 3089, 1, 2339, 1, 322727, 1, 325019, 40771, 327319, 2161, 329627, 10337, 331943, 1, 1, 1823, 336599, 42221, 4643, 1, 341287, 5351, 1, 43103, 1933, 43399, 3083, 2731, 18461, 21997, 353147, 44293, 2129, 2347, 12343, 22447, 2083, 11299, 15773, 1, 5987, 1, 1, 11527, 6067, 1, 372539, 2459, 1, 1, 3463, 23669, 19997, 1489, 382427, 1, 384919, 48271, 1621, 6073, 389927, 1, 392443, 1697, 394967, 49529, 20921, 24923, 17393, 12541, 402587, 2657, 405143, 1, 407707, 12781, 410279, 1, 412859, 51769, 415447, 1, 418043, 26209, 18289, 1, 423259, 1, 425879, 1, 1, 1, 14867, 1, 433787, 1, 436439, 54721, 1, 27527, 4289, 1, 444443, 1, 1, 1, 15511, 1, 452519, 1493, 455227, 57073, 457943, 57413, 20029, 1, 463399, 3631, 466139, 58439, 468887, 2027, 4327, 1, 3413, 1, 1, 1, 25261, 60169, 1, 30259, 485543, 15217, 488347, 2111, 491159, 2677, 493979, 1, 1889, 31139, 26297, 62633, 502487, 62989, 505339, 1667, 1, 7963, 17623, 64063, 513943, 2801, 2011, 4049, 7757, 32573, 2243, 1, 1, 3467, 8663, 33119, 1, 16651, 1, 1, 3217, 67339, 540187, 16927, 543143, 34039, 5407, 68449, 23873, 68821, 552059, 1, 1, 1, 8329, 3041, 561047, 3701, 564059, 8837, 2969, 35537, 570107, 71453, 573143, 2477, 5099, 36107, 579239, 18149, 582299, 1, 585367, 73363, 2957, 1, 1, 1, 1, 74521, 20611, 1, 600827, 37649, 3491, 9461, 607067, 76079, 610199, 76471, 1699, 1, 1, 38629, 1, 1, 1, 78049, 625979, 1, 2239, 1, 632347, 1, 4639, 1, 2357, 20011, 641959, 1, 645179, 80849, 2713, 1, 34297, 40829, 4337, 1, 658139, 82471, 1, 1, 664667, 1, 1, 41849, 3373, 1, 1, 84521, 2447, 42467, 681127, 1, 684443, 1, 687767, 86179, 23831, 21649, 1, 1, 697787, 87433, 3917, 87853, 704507, 1, 5167, 11087, 711259, 89119, 1, 1, 718043, 5623, 11827, 45197, 1, 90821, 11939, 91249, 1, 1993, 735143, 23027, 38873, 3191, 3079, 1, 32413, 1, 1, 46919, 2861, 94273, 1, 94709, 1, 1, 762919, 1, 10499, 1, 769943, 5077, 33629, 12113, 11597, 48673, 41081, 97789, 784087, 4271, 2803, 49339, 27283, 24781, 794779, 99571, 3517, 100019, 801947, 25117, 42397, 50459, 809147, 1, 812759, 1, 28151, 51137, 7523, 12841, 823643, 103183, 35969, 1, 830939, 3253, 834599, 1, 1, 5527, 3709, 3637, 2423, 52967, 44701, 1, 1, 106859, 1, 107323, 1, 26947, 864167, 1, 5197, 1, 871639, 1,

6. Sequence of the polynom (only primes)

613, 23, 857, 61, 1093, 151, 1321, 179, 67, 103, 1753, 29, 19, 257, 2153, 281, 2341, 2521, 163, 2693, 347, 2857, 367, 131, 193, 109, 101, 3301, 421, 3433, 3557, 113, 3673, 233, 199, 479, 3881, 491, 137, 251, 4057, 4133, 521, 4201, 4261, 227, 271, 4357, 547, 191, 4421, 277, 4441, 139, 73, 557, 4457, 167, 443, 727, 1019, 1319, 1627, 223, 263, 2267, 173, 2939, 389, 433, 3643, 239, 4007, 571, 4759, 619, 5147, 241, 359, 313, 769, 6359, 821, 6779, 7207, 7643, 983, 8087, 1039, 8539, 8999, 577, 9467, 1213, 10427, 349, 601, 1459, 11927, 1523, 541, 397, 12967, 827, 13499, 1721, 1789, 503, 929, 797, 1999, 733, 1109, 18043, 2293, 643, 19259, 1223, 631, 20507, 21143, 2683, 21787, 691, 1181, 1423, 23099, 23767, 24443, 1549, 25127, 25819, 3271, 1153, 3359, 1433, 431, 27943, 29399, 30139, 1907, 461, 977, 31643, 4003, 1409, 4099, 33179, 1049, 1171, 34747, 35543, 4493, 1913, 2297, 37159, 587, 4799, 4903, 1367, 40487, 2557, 617, 2221, 43067, 2719, 43943, 1949, 5659, 46619, 1471, 47527, 2999, 6113, 49367, 6229, 51239, 2269, 2797, 6703, 887, 853, 55079, 919, 7069, 57047, 7193, 58043, 3659, 1861, 593, 7699, 64187, 8089, 65239, 8221, 4177, 1061, 68443, 8623, 70619, 71719, 4517, 3833, 9173, 73943, 3313, 2399, 77339, 9739, 78487, 9883, 1091, 4253, 5087, 1123, 10321, 607, 84347, 5309, 653, 673, 87959, 11071, 90407, 5689, 811, 3203, 11689, 4093, 5923, 5021, 3001, 96667, 12163, 97943, 12323, 1481, 3121, 100519, 6323, 3511, 12809, 12973, 6569, 105767, 1663, 107099, 709, 108439, 1087, 863, 111143, 112507, 14149, 14321, 115259, 7247, 1741, 118043, 14843, 119447, 6361, 122279, 7687, 123707, 5441, 15733, 1229, 2099, 129499, 4567, 2081, 17021, 5953, 17209, 138427, 8699, 139943, 4397, 773, 4931, 17971, 144539, 18553, 7853, 18749, 150779, 9473, 1009, 2393, 153947, 1427, 19543, 941, 158759, 9973, 20149, 162007, 20353, 163643, 165287, 1201, 168599, 21179, 170267, 5347, 1237, 10799, 7549, 881, 177019, 11117, 6163, 9497, 182167, 1063, 2887, 2543, 11657, 187387, 2591, 23753, 11987, 10141, 1193, 24419, 196247, 1297, 198043, 6217, 8689, 12547, 25321, 3037, 205307, 12889, 3251, 2029, 1381, 210839, 937, 1669, 13469, 2143, 2003, 27409, 6971, 224027, 28123, 225943, 7151, 229799, 14423, 1531, 233687, 29333, 3863, 237607, 239579, 30071, 241559, 30319, 10589, 3821, 8467, 247547, 31069, 31321, 13241, 15787, 253607, 1693, 32083, 257687, 261799, 16427, 263867, 33113, 13997, 1451, 1987, 34159, 1187, 276443, 1709, 17477, 280699, 35221, 2503, 1543, 2843, 9007, 1499, 36299, 36571, 293659, 295847, 298043, 300247, 302459, 18973, 2389, 13441, 38783, 2377, 313639, 315899, 1723, 3089, 2339, 322727, 325019, 40771, 327319, 2161, 329627, 10337, 331943, 1823, 336599, 42221, 4643, 341287, 5351, 43103, 1933, 43399, 3083, 2731, 18461, 21997, 353147, 44293, 2129, 2347, 12343, 22447, 2083, 11299, 15773, 5987, 11527, 6067, 372539, 2459, 3463, 23669, 19997, 1489, 382427, 384919, 48271, 1621, 6073, 389927, 392443, 1697, 394967, 49529, 20921, 24923, 17393, 12541, 402587, 2657, 405143, 407707, 12781, 410279, 412859, 51769, 415447, 418043, 26209, 18289, 423259, 425879, 14867, 433787, 436439, 54721, 27527, 4289, 444443, 15511, 452519, 1493, 455227, 57073, 457943, 57413, 20029, 463399, 3631, 466139, 58439, 468887, 2027, 4327, 3413, 25261, 60169, 30259, 485543, 15217, 488347, 2111, 491159, 2677, 493979, 1889, 31139, 26297, 62633, 502487, 62989, 505339, 1667, 7963, 17623, 64063, 513943, 2801, 2011, 4049, 7757, 32573, 2243, 3467, 8663, 33119, 16651, 3217, 67339, 540187, 16927, 543143, 34039, 5407, 68449, 23873, 68821, 552059, 8329, 3041, 561047, 3701, 564059, 8837, 2969, 35537, 570107, 71453, 573143, 2477, 5099, 36107, 579239, 18149, 582299, 585367, 73363, 2957, 74521, 20611, 600827, 37649, 3491, 9461, 607067, 76079, 610199, 76471, 1699, 38629, 78049, 625979, 2239, 632347, 4639, 2357, 20011, 641959, 645179, 80849, 2713, 34297, 40829, 4337, 658139, 82471, 664667, 41849, 3373, 84521, 2447, 42467, 681127, 684443, 687767, 86179, 23831, 21649, 697787, 87433, 3917, 87853, 704507, 5167, 11087, 711259, 89119, 718043, 5623, 11827, 45197, 90821, 11939, 91249, 1993, 735143, 23027, 38873, 3191, 3079, 32413, 46919, 2861, 94273, 94709, 762919, 10499, 769943, 5077, 33629, 12113, 11597, 48673, 41081, 97789, 784087, 4271, 2803, 49339, 27283, 24781, 794779, 99571, 3517, 100019, 801947, 25117, 42397, 50459, 809147, 812759, 28151, 51137, 7523, 12841, 823643, 103183, 35969, 830939, 3253, 834599, 5527, 3709, 3637, 2423, 52967, 44701, 106859, 107323, 26947, 864167, 5197, 871639,

7. Distribution of the primes

Legend of the table: I distinguish between primes p= x^2-124x-613 and
the reducible primes which appear as divisor for the first time
p | x^2-124x-613 and p < x^2-124x-613

To avoid confusion with the number of primes:
I did not count the primes <= A
but I counted the primes appending the x and therefore the x <= A

A B C D E F G H
exponent
=log2 (x)
<=x number
of all primes
number of primes
p = f(x)
number of primes
p | f(x)
C / x D / x E / x
1 2 3 2 1 1.5 1 0.5
2 4 5 3 2 1.25 0.75 0.5
3 8 9 4 5 1.125 0.5 0.625
4 16 17 7 10 1.0625 0.4375 0.625
5 32 31 13 18 0.96875 0.40625 0.5625
6 64 57 23 34 0.890625 0.359375 0.53125
7 128 57 23 34 0.4453125 0.1796875 0.265625
8 256 148 62 86 0.578125 0.2421875 0.3359375
9 512 330 116 214 0.64453125 0.2265625 0.41796875
10 1024 694 222 472 0.67773438 0.21679688 0.4609375
11 2048 1428 411 1017 0.69726563 0.20068359 0.49658203
12 4096 2866 753 2113 0.69970703 0.18383789 0.51586914
13 8192 5752 1345 4407 0.70214844 0.16418457 0.53796387
14 16384 11531 2505 9026 0.70379639 0.15289307 0.55090332
15 32768 23080 4636 18444 0.7043457 0.14147949 0.56286621
16 65536 46122 8683 37439 0.70376587 0.13249207 0.5712738
17 131072 92280 16099 76181 0.70404053 0.12282562 0.5812149
18 262144 184460 30283 154177 0.70365906 0.11552048 0.58813858
19 524288 368565 57264 311301 0.70298195 0.10922241 0.59375954
20 1048576 736658 108102 628556 0.70253181 0.1030941 0.59943771
21 2097152 1472550 205112 1267438 0.70216656 0.09780502 0.60436153
22 4194304 2943637 390077 2553560 0.70181775 0.0930016 0.60881615
23 8388608 5884286 743310 5140976 0.70146155 0.08860946 0.6128521
24 16777216 11761893 1420374 10341519 0.70106345 0.08466089 0.61640257


8. Check for existing Integer Sequences by OEIS

Found in Database : 613, 23, 857, 61, 1093, 151, 1321, 179, 67, 103, 1753, 29, 19, 257, 2153, 281, 2341, 1, 2521, 163,
Found in Database : 613, 23, 857, 61, 1093, 151, 1321, 179, 67, 103, 1753, 29, 19, 257, 2153, 281, 2341, 2521, 163, 2693, 347, 2857, 367, 131, 193, 109, 101, 3301, 421, 3433, 3557, 113, 3673, 233, 199, 479, 3881, 491,
Found in Database : 19, 23, 29, 61, 67, 73, 101, 103, 109, 113, 131, 137, 139,