Sum of Consecutive Prime Numbers Under 1000

List of all prime numbers under 1000:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997

 
2 + 3 = 5

7
11
13

2 + 3 + 5 + 7 = 17
and the reverse of 17,   71 = 19 + 23 + 29

19

5 + 7 + 11 = 23

29

7 + 11 + 13 = 31

37

11 + 13 + 17 = 41       3 + 7 + 31 = 41
2 + 3 + 5 + 7 + 11 + 13 = 41

Forming 3 sums of primes with the prime value of 43 using the 10 first primes
2+5+7+29 = 3+17+23 = 11+13+19 = 43

2 + 3 + 5 + 7 + 11 + 19 = 47
5 + 7 + 11 + 13 + 17 = 53
17 + 19 + 23 = 59
13 + 17 + 31 = 61
7 + 11 + 13 + 17 + 19 = 67
19 + 23 + 29 = 71
19 + 23 + 31 = 73

11 + 31 + 37 = 79
The sum holds for the reversals:    11 + 13 + 73 = 97
29 + 31 + 37 = 97

23 + 29 + 31 =   83   = 11 + 13 + 17 + 19 + 23

89

29 + 31 + 37 = 97

13 + 17 + 19 + 23 + 29 = 101

103
107
31 + 37 + 41 = 109

Forming 7 sums of primes with the prime value of 113 using the first 22 primes:
2+19+31+61=3+37+73=5+41+67=7+47+59=11+23+79=13+29+71=17+43+53= 113

3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 127

41 + 43 + 47 = 131

137

19 + 23 + 29 + 31 + 37 = 139
23 + 43 + 83 = 149

151
157

37 + 59 + 67 = 163

167

53 + 59 + 61 = 173

179

29 + 31 + 37 + 41 + 43 = 181

191
193

17 + 19 + 23 + 29 + 31 + 37 + 41 = 197
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 = 197

61 + 67 + 71 = 199
31 + 37 + 41 + 43 + 47 = 199

67 + 71 + 73 = 211

19 + 23 + 29 + 31 + 37 + 41 + 43 = 223

227
229

5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 = 233

239
241

79 + 83 + 89 = 251
23 + 29 + 31 + 37 + 41 + 43 + 47 = 251

257

43 + 47 + 53 + 59 + 61 = 263

83 + 89 + 97 = 269

7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 271

277

29 + 31 + 37 + 41 + 43 + 47 + 53 = 281
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 281

283
293
307

31 + 37 + 41 + 43 + 47 + 53 + 59 = 311

313
317
331
337
347
349

13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53= 353

5 + 17 + 31 + 79 + 227 = 359

367
373
379

53 + 157 + 173 = 383

389
397
401
409
419
421
431
433
439
443
449
457
461
463
467
479
487
491
499
503
509
521
523
541
547
557
563
569
571
577
587
593
599
601
607
613
617
619
631
641
643
647
653
659
661
673
677
683
691
701
709
719
727
733

3 + 353 + 383 = 739

743
751
757
761
769

2 + 3 + 11 + 13 + 127 + 617 = 773

787
797
809

151 + 157 + 163 + 167 + 173 = 811

821
823
827
829
839
853
857
859

29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 = 863

877
881
883
887
907
911
919
929
937
941

89 + 409 + 449 = 947

7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83+89 = 953
when arranged in groups of three, each group sums to a prime
(7+11+13)+(17+19+23)+(29+31+37)+(41+43+47)+(53+59+61)+(67+71+73)+(79+83+89)
7 + 11 + 13 = 31
17 + 19 + 23 = 59
29 + 31 + 37 = 97
41 + 43 + 47 = 131
53 + 59 + 61 = 173
67 + 71 + 73 = 211
79 + 83 + 89 = 251

967
971
977
983
991
997

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Math Beauty and tagged , . Bookmark the permalink.

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