Welcome to Prime Number Codes. We hope it will be useful in your enjoyment of prime research. If you aleady have a list of primes the codes may not be very useful, however codes are stored in one-third the hardware/software space as primes, and after one division step, codes take as much time to look up as primes. Learn about the codes anyway, its more fun, and easy as one, two, three!.
Say you have a friend over and begin to discuss some heavy duty math projects, and you challenge each other to see how fast you can come up with the answer to the question: is 299209 a prime number, and assume that neither of you has a list of primes or a computer program to do it? Well, division by 30 will result in a quotient that contains a code to nail it quickly, say within 5 or 6 seconds, whereas it will take more than 100 division steps otherwise. Cool, huh?
PRIMES AS EASY AS ONE, TWO, THREE:
Step 1. Divide the test number by 30.
Step 2. The quotient identifies a row on the left of the decimal, the decimal identifies a code, as follows:
Decimal Code
.033 1
.233 2
.366 3
.433 4
.566 5
.633 6
.766 7
.966 8
Step 3. Go to the Prime Code Tables, find the row and associated codes, if the code is there the test number is prime. For example, if the code is 1 (for decimal .033) and the codes for the row include the digit 1, the tested number is prime. Note that any decimal other than one of the eight shown above identifies a composite.
Use the above instruction steps to review the following examples using the Prime Codes table below.
Example 1. Test number 143; division gives 143/30 = 4.766, indicating row 4 code 7. In the table there is no 7 among the codes for row 4 (23568) thus 143 is composite.
Example 2. Test number 6269; division gives 6269/30 = 208.966, indicating row 208 and code 8. Go to column 200+ in the table and down to row 8 (200+8 = 208) and the acceptable codes (2578) include an 8, thus the test number 6269 is prime.
Example 3. Test number 7131; division gives 7131/30 = 237.700, for row 237 but .700 is not one of the eight acceptable decimals, and thus 7131 is composite.
Prime Codes for Row 0 to 250
0+ 50+ 100+ 150+ 200+
0 2345678 37 1367 24567 238
1 1234578 14678 236 56 2457
2 1234678 2367 12678 127 2468
3 234567 235678 68 124 137
4 23568 125 15 15678 1347
5 124578 2456 456 12478 147
6 13456 4568 12378 37 567
7 145678 347 236 3467 1236
8 13578 1246 3456 36 2578
9 12347 2456 18 45678 1258
10 2345 137 124678 145 13578
11 125678 15 1458 1 2478
12 24678 1234568 1348 1358 12468
13 2368 357 157 2567 2
14 134678 348 48 3457 128
15 23458 178 23456 12567 167
16 23678 24567 36 24678 13
17 34 12568 125678 1348 36
18 12578 478 1256 36 23478
19 12578 34568 1347 2358 1238
20 12456 348 2457 1246 26
21 134578 12347 1248 57 278
22 1457 16 345 2368 1468
23 1368 457 12368 26 13468
24 2467 1567 246 2345 45
25 12367 1567 3568 378 348
26 258 12458 457 1578 1347
27 13468 178 347 47 4567
28 4567 1235 2347 23 1578
29 2345 1234678 236 3578 148
30 2368 357 235678 2456 235
31 2357 2358 145 12346 68
32 2357 245 28 3567 12357
33 12678 4 34578 3458 12378
34 13468 13678 128 123 267
35 1346 128 1278 2467 268
36 234578 347 346 13 78
37 246 237 15678 48 356
38 347 2567 456 1234568 36
39 1357 1245678 2 467 257
40 14578 23468 13568 135 23468
41 1268 1367 13478 2346 2457
42 5678 258 13478 67 7
43 123458 12346 2 1357 256
44 12 457 2568 12678 1348
45 357 1238 247 123568 16
46 168 2578 358 157 4
47 45678 258 34 458 127
48 2346 4578 12357 4 356
49 1345678 18 347 35 23568
50 37 1367 24567 238 2578
The above codes cover primes through 10K and codes are now available for primes through 1M in booklet form or floppy for use in the classroom or light industry. Email us at ki@kispy.net (use the word "codes" in the subject) for an update, more info, or request copies as work continues to get codes through 10M as well as a computer program to facilitate the process. Unfortunately, primes above 100M will not work well because of rounding.
On a personal note, I have been in and out of primes for over 50 years, and got an eye-opener these last three after finally getting together with a few others on the internet. (G.L.Honaker with Prime Curios has been a great coach.) My pursuit was to find a method of testing numbers for primality with only one division step, which was finally achieved these last few months after looking over some of my old notes. I need help to computerize the entire process, so interested readers are welcome to offer assistance.
Ki the Spy
An alternate method to find the codes is by SOD (sum of digits.)
Step 1. If SOD evenly divides by 3, the number is composite.
Step 2. For test numbers that end in:
1, if (SOD -1)/3 is integer, the code is 1, otherwise 3.
3, if (SOD-1)/3 is integer, the code is 4, otherwise 7.
7, if (SOD-1)/3 is integer, the code is 2, otherwise 5.
9, if (SOD-1)/3 is integer, the code is 6, otherwise 8.