Block #208,374

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/13/2013, 11:27:50 PM · Difficulty 9.9062 · 6,584,184 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

63446090759299866d65f5cb358a96aae87cc322e98f3918eadaa7f1d23f0e5d

View on Chainz ↗

Height

#208,374

Difficulty

9.906154

Transactions

Size

199 B

Version

Bits

09e7f9b1

Nonce

68,483

Timestamp

10/13/2013, 11:27:50 PM

Confirmations

6,584,184

Merkle Root

f0b7afaddf115716b9d435ff107730c0e6b593bdc4368ffe3f6c327779841546

Transactions (1)

Coinbasef0b7afaddf1157…6c327779841546

1 in → 1 out10.1800 XPM109 B

ATK4r8Gh…Usic4A9N

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.

1.447 × 10⁹⁴(95-digit number)

14470304692644506142…90908389087626025841

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

1.447 × 10⁹⁴(95-digit number)

14470304692644506142…90908389087626025841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.894 × 10⁹⁴(95-digit number)

28940609385289012284…81816778175252051681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.788 × 10⁹⁴(95-digit number)

57881218770578024568…63633556350504103361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.157 × 10⁹⁵(96-digit number)

11576243754115604913…27267112701008206721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.315 × 10⁹⁵(96-digit number)

23152487508231209827…54534225402016413441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.630 × 10⁹⁵(96-digit number)

46304975016462419654…09068450804032826881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.260 × 10⁹⁵(96-digit number)

92609950032924839309…18136901608065653761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.852 × 10⁹⁶(97-digit number)

18521990006584967861…36273803216131307521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.704 × 10⁹⁶(97-digit number)

37043980013169935723…72547606432262615041

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