Chen Prime Calculator

Input a number to check if it is a Chen prime, or input a start and end range to generate all Chen primes within that range.

Chen Prime Check or Generate

What is a Chen Prime?

A Chen prime is a prime number \(p\) that satisfies the following condition: \(p+2\) is either a prime number or a semiprime (the product of exactly two primes).

Using this definition, you can determine if a number is a Chen prime or generate a list of Chen primes.

How to Determine if a Number is a Chen Prime

To check if a given number \(p\) is a Chen prime, follow these steps:

  1. Check if \(p\) is a prime number: If \(p\) is not a prime number, it is not a Chen prime.
  2. Calculate \(p+2\):
    • If \(p+2\) is a prime, \(p\) is a Chen prime.
    • If \(p+2\) is a semiprime (the product of two primes), \(p\) is still a Chen prime.

Examples

Example 1: Check if 101 is a Chen prime

Solution:

1. Is 101 a prime number?

Yes, 101 is a prime number.

2. Calculate \(101 + 2 = 103\).

103 is also a prime number.

Result: 101 is a Chen prime.

Example 2: Check if 199 is a Chen prime

Solution:

1. Is 199 a prime number?

Yes, 199 is a prime number.

2. Calculate \(199 + 2 = 201\).

201 is not a prime number; it is a semiprime (\(201 = 3 \times 67\)).

Result: 199 is a Chen prime.

Example 3: Check if 397 is a Chen prime

Solution:

1. Is 397 a prime number?

Yes, 397 is a prime number.

2. Calculate \(397 + 2 = 399\).

399 is neither a prime number nor a semiprime (\(399 = 3 \times 7 \times 19\)).

Result: 397 is not a Chen prime.

The First 100 Chen Primes

  • 2
  • 3
  • 5
  • 7
  • 11
  • 13
  • 17
  • 19
  • 23
  • 29
  • 31
  • 37
  • 41
  • 47
  • 53
  • 59
  • 67
  • 71
  • 83
  • 89
  • 101
  • 107
  • 109
  • 113
  • 127
  • 131
  • 137
  • 139
  • 149
  • 157
  • 167
  • 179
  • 181
  • 191
  • 197
  • 199
  • 211
  • 227
  • 233
  • 239
  • 251
  • 257
  • 263
  • 269
  • 281
  • 293
  • 307
  • 311
  • 317
  • 337
  • 347
  • 353
  • 359
  • 379
  • 389
  • 401
  • 409
  • 419
  • 431
  • 443
  • 449
  • 461
  • 467
  • 479
  • 487
  • 491
  • 499
  • 503
  • 509
  • 521
  • 541
  • 557
  • 563
  • 569
  • 571
  • 577
  • 587
  • 599
  • 617
  • 631
  • 641
  • 647
  • 653
  • 659
  • 677
  • 683
  • 701
  • 719
  • 743
  • 751
  • 761
  • 769
  • 787
  • 797
  • 809
  • 811
  • 821
  • 827
  • 829
  • 839