Thursday, March 26, 2020

Sums of Primes


11 + 13 + 17 + 19 + 23 + 29 + 31 = 143 = 11 × 13
37 + 41 + 43 + 47 + 53 + 59 + 61 = 341 = 11 × 31
67 + 71 + 73 + 79 + 83 + 89 + 97 = 559 = 13 × 43
101 + 103 + 107 + 109 = 420 // 24
113 + 127 + 131 + 137 = 508 // 31

#2) 11 + 13 = 24
#4) 11 + 13 + 17 + 19 = 60
17) 11 + . . . + 73 = 695 = 5 × 139=PR#30
29) 1971 = 3 × 3 × 3 × 73  // 197 = PR#41
1973 = PR#294,
00 + 60 + 695 + 1971 = 2726 = 2 × 29 × 47.
24 + 60 + 695 + 1971 = 2750 = 2 × 25 × 55.
24 + 24 + 695 + 1971 = 2714 = 2 × 23 × 59.

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Sum digits 11 - 97 ) 1043 = 7 × 149
Sum cifers 11 - 97 ) 44+62+91 = 197
1+1 + 1+3 + 1+7 + 1+9 + 2+3 + 2+9 + 3+1 = 44
3+7 + 4+1 + 4+3 + 4+7 + 5+3 + 5+9 + 6+1 = 62
6+7 + 7+1 + 7+3 + 7+9 + 8+3 + 8+9 + 9+7 = 91
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1) Primes# 1 - 22
311 + 833 = 1144 = 88 × 13, 
1144 - 101 = 1043 = 7 × 149=PR#31
PR# 22 - 44) 3500
PR# 45 - 66) 6226 = 22×283
PR# 67 - 88) 9172 = 46^2 + 84^2

2) Primes# 23 - 132
46661 - 101 = 46560 = 240 × 97 × 2 = 6^6 - 96.
46661 = 29 × 1609 . 1609 = PR#250.
46661 = 6^6 + 5 = 65^2 + 206^2 = 95^2 + 194^2.

3) Primes# 133 - 242
128088 = 8 × 27 × 593=PR#104

4) Primes# 243 - 352
218408 = 8 × 23 × 1187=PR#191

5) Primes# 353 - 462
311157 = 9×7×11×449=PR#83

6) Primes# 463 - 572
412370 = 2×5×7×43×137=PR#29

7) Primes# 573 - 682
514396 = 4×128599 = 207×71×5×7 + 1

8) Primes# 683 - 792
619178# = 2×7×47×941=PR#156  ,, 2253444 = 12 × 187787

9) Primes# 793 - 902
724152 = 2×13×211×11×2×3×1×2

10) Primes# 903 - 1012
833378 = 19×7×2×13×241=PR#49

11) Primes# 1013 - 1122
180048 + 184384 + 189248 + 193030 + 197342 = 
944052 = 12×151×521

All - 4755026

PR#1-1233) 5816729 = 307 × 18947 , 568 = 2 × 2 × 2 × 71.
PR#1-1122) 4755026 = 2 × 43 × 55291 > Paul numbers

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PR#1-188 > (11-1163) SUM = 101984 - 101501 = 483 = 3 × 7 × 23

PR#1-462 > 707500 - 710507 = 3007 = 31 × 97
PR#1-463 > 710819 - 710507 = 312   = 24 × 13

PR#40-464 > 710521 - 710507 = 14 (424PR)

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Primes #3450  - #3471

32191+32203+32213+32233+32237+32251+32257+32261+32297+32299+32303+
32309+32321+32323+32327+32341+32353+32359+32363+32369+32371+32377 =
710558 = 2 × 29 × 12251-PR#1460
710507 = 7 × 101501


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PR#1972 = 17159 (314159) (17150 = 343 * 50)
2*17159 + 1 = 34319 = PR#3664 (343 + 16)
95171 = 19 × 5009


PR#1968 - #1976, sum 154373 = PR#14219
17107 17117 17123 17137 17159 17167 17183 17189 17191

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Primes # 9712 - 9726
101449 101477 101483 101489 101501 
101503 101513 101527 101531 101533 
101537 101561 101573 101581 101599

10487 = PR#1279
10663 = PR#1297
14783 = PR#1729
15373 = PR#1792
16693 = PR#1927
17159 = PR#1972
19249 = PR#2179
19427 = PR#2197
24547 = PR#2719
25343 = PR#2791
26641 = PR#2917
27127 = PR#2971
72053 = PR#7129
72763 = PR#7192
73039 = PR#7219
73907 = PR#7291
80897 = PR#7912
80989 = PR#7921
94693 = PR#9127
95203 = PR#9172
95633 = PR#9217
96281 = PR#9271
101449 = PR#9712 + 52
101501 = PR#9716 + 32
101533 = PR#9721

710507 - 101533 = 608974 = 2 × 17 × 17911
710507 - 101449 = 609058 = 2 × 29 × 10501
710507 -   96281 = 614226 = 2 × 3 × 167 × 613

9716 = 7×4×347.

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Sums of Primes up to #1972, numbers in brackets.

( 1 - 9999 ) 5736361 = 17^2×23×863
( 10000 ) 1112190 = 2×3×5×131×283
( 11000 - 12000 ) 2548606 = 2×17×74959
( 13000 - 14000 ) 2888777 = 23×29×61×71
( 15000 - 16000 ) 3290640 = 16×3×5×13711
( 17011 - 17159 ) 273174 = 66×4139
5816729 + 10033019 = 15849748 = 4×3962437
( 11 - 10079 ) 5816729 = 307 × 18947
( 10091 - 17159 ) 10033019 = PR#666631

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