Strong Prime Checker is a free online tool used to check if the given number is a strong prime.
What is a strong prime?
A strong prime number is a prime number whose value is greater than the arithmetic mean of the nearest prime number before and after the number in the prime sequence. A strong prime is closer to the following prime rather than the preceding prime.
It can be represented as
pn > (pn − 1 + pn + 1)2
For example, consider the prime 101.
The first prime number before 101 is 97 and the next prime number after 101 is 103. The arithmetic mean of them is
(97 + 103)2 = 2002 = 100
101 is greater than 100. So, 101 is a strong prime.
First 100 strong primes
- 11
- 17
- 29
- 37
- 41
- 59
- 67
- 71
- 79
- 97
- 101
- 107
- 127
- 137
- 149
- 163
- 179
- 191
- 197
- 223
- 227
- 239
- 251
- 269
- 277
- 281
- 307
- 311
- 331
- 347
- 367
- 379
- 397
- 419
- 431
- 439
- 457
- 461
- 479
- 487
- 499
- 521
- 541
- 557
- 569
- 587
- 599
- 613
- 617
- 631
- 641
- 659
- 673
- 701
- 719
- 727
- 739
- 751
- 757
- 769
- 787
- 809
- 821
- 827
- 853
- 857
- 877
- 881
- 907
- 929
- 937
- 967
- 991
- 1009
- 1019
- 1031
- 1049
- 1061
- 1087
- 1091
- 1117
- 1151
- 1163
- 1181
- 1213
- 1229
- 1249
- 1277
- 1289
- 1297
- 1301
- 1319
- 1361
- 1399
- 1423
- 1427
- 1447
- 1451
- 1471
- 1481
How to use the strong prime checker
The procedure to use the strong prime checker is as follows:
- Enter the positive integer.
- Click Calculate button to verify whether the input integer is a strong prime.
- Click the Reset button to start a new verification.
Solved examples using the strong prime checker
Example 1: Is 211 a strong prime?
Enter 211 into the input box and click Calculate button, as shown in the figure, 211 is not a strong prime.
199 + 2232 = 211
Example 2: Is 1997 a strong prime?
Enter 1997 into the input box and click Calculate button, as shown in the figure, 1997 is a strong prime.
1993 + 19992 = 1996
1997 is greater than 1996. So, 1997 is a strong prime.
Latest Checkers
Check if the given number is an almost perfect number.
Latest Calculators
Standard Form to Slope-Intercept Form Calculator
Slope Intercept Form Calculator
Slope Calculator: Calculate Slope, X-Intercept, Y-Intercept
Reciprocal of Complex Number Calculator
Conjugate Complex Number Calculator
Modulus of Complex Number Calculator
Profit Percentage Calculator: Calculate Your Profitability Easily
Attendance and Absence Percentage Calculator