Block #75,502

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 4:51:33 PM · Difficulty 9.0100 · 6,721,324 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

3418b6f876518983c06c46f5b706a664ca5d65d7471711802c770cc12e42098d

View on Chainz ↗

Height

#75,502

Difficulty

9.010036

Transactions

Size

838 B

Version

Bits

090291bc

Nonce

702

Timestamp

7/21/2013, 4:51:33 PM

Confirmations

6,721,324

Mined by

⛏️ P2SHAQSbGiRbD2vuhtmALtc7GEd5y7RkHowpJS

Merkle Root

b8015aa9d230d563034b6cdd7730ac6e86a2a35a7ed3c44ecc0106c2ec9e79f5

Transactions (2)

Coinbaseb1d44bf6d568ea…1629f504d07949

1 in → 1 out12.3100 XPM110 B

AQSbGiRb…RkHowpJS

d786cdddf5095d…ab050921de9d53

4 in → 1 out799.9000 XPM636 B

APE1dWFB…3PrGLeMk

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.792 × 10⁹⁹(100-digit number)

57925933008684201983…60313615405948055201

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

5.792 × 10⁹⁹(100-digit number)

57925933008684201983…60313615405948055201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.158 × 10¹⁰⁰(101-digit number)

11585186601736840396…20627230811896110401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.317 × 10¹⁰⁰(101-digit number)

23170373203473680793…41254461623792220801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.634 × 10¹⁰⁰(101-digit number)

46340746406947361586…82508923247584441601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.268 × 10¹⁰⁰(101-digit number)

92681492813894723172…65017846495168883201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.853 × 10¹⁰¹(102-digit number)

18536298562778944634…30035692990337766401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.707 × 10¹⁰¹(102-digit number)

37072597125557889269…60071385980675532801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.414 × 10¹⁰¹(102-digit number)

74145194251115778538…20142771961351065601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.482 × 10¹⁰²(103-digit number)

14829038850223155707…40285543922702131201

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer