Block #315,705

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/16/2013, 3:51:49 PM · Difficulty 10.1122 · 6,500,379 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

856b09bf29a1a91e69d182d1b8256b46caa4950b26a6a20751ccc4d070495a67

View on Chainz ↗

Height

#315,705

Difficulty

10.112190

Transactions

Size

205 B

Version

Bits

0a1cb87d

Nonce

5,597

Timestamp

12/16/2013, 3:51:49 PM

Confirmations

6,500,379

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a1d5589a81818083d0b9204241343911b5c924978407f23cf24fc516a6b5863b

Transactions (1)

Coinbasea1d5589a818180…4fc516a6b5863b

1 in → 1 out9.7600 XPM116 B

AbwWkWZt…kawDhufa

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.

6.608 × 10⁹¹(92-digit number)

66083514343294040128…15040634277827817761

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

6.608 × 10⁹¹(92-digit number)

66083514343294040128…15040634277827817761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.321 × 10⁹²(93-digit number)

13216702868658808025…30081268555655635521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.643 × 10⁹²(93-digit number)

26433405737317616051…60162537111311271041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.286 × 10⁹²(93-digit number)

52866811474635232103…20325074222622542081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.057 × 10⁹³(94-digit number)

10573362294927046420…40650148445245084161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.114 × 10⁹³(94-digit number)

21146724589854092841…81300296890490168321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.229 × 10⁹³(94-digit number)

42293449179708185682…62600593780980336641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.458 × 10⁹³(94-digit number)

84586898359416371365…25201187561960673281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.691 × 10⁹⁴(95-digit number)

16917379671883274273…50402375123921346561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.383 × 10⁹⁴(95-digit number)

33834759343766548546…00804750247842693121

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

Block #315,705

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