Block #358,745

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/14/2014, 7:55:25 AM · Difficulty 10.3844 · 6,434,028 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7c69ba378843076b728e4c0d02b419854f966607da5989008184348da7469bd5

View on Chainz ↗

Height

#358,745

Difficulty

10.384387

Transactions

Size

597 B

Version

Bits

0a626738

Nonce

74,308

Timestamp

1/14/2014, 7:55:25 AM

Confirmations

6,434,028

Merkle Root

c87caaba4f6a9a13256e6de8fa62d80dacd6b94ded82ce961c2c4425a0df402e

Transactions (1)

Coinbasec87caaba4f6a9a…2c4425a0df402e

1 in → 13 out9.2600 XPM505 B

AN9emqpK…WEnrfX7s Ac5JXwCr…tf5C9dQa AFutDVqJ…TJTJj6UF ATdV4gn5…qCyGeGw1 AJdLNXdT…prit4boi

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.

8.156 × 10⁹⁹(100-digit number)

81563715646435387357…75864151993558876161

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

8.156 × 10⁹⁹(100-digit number)

81563715646435387357…75864151993558876161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.631 × 10¹⁰⁰(101-digit number)

16312743129287077471…51728303987117752321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.262 × 10¹⁰⁰(101-digit number)

32625486258574154942…03456607974235504641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.525 × 10¹⁰⁰(101-digit number)

65250972517148309885…06913215948471009281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.305 × 10¹⁰¹(102-digit number)

13050194503429661977…13826431896942018561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.610 × 10¹⁰¹(102-digit number)

26100389006859323954…27652863793884037121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.220 × 10¹⁰¹(102-digit number)

52200778013718647908…55305727587768074241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.044 × 10¹⁰²(103-digit number)

10440155602743729581…10611455175536148481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.088 × 10¹⁰²(103-digit number)

20880311205487459163…21222910351072296961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.176 × 10¹⁰²(103-digit number)

41760622410974918326…42445820702144593921

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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