Block #474,736

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/4/2014, 6:21:21 PM · Difficulty 10.4558 · 6,367,163 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c051edc8dc488c199b524d5c9faa4e32a28cedb107375107d203264ce0614475

View on Chainz ↗

Height

#474,736

Difficulty

10.455797

Transactions

Size

202 B

Version

Bits

0a74af15

Nonce

493,701

Timestamp

4/4/2014, 6:21:21 PM

Confirmations

6,367,163

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

758f5eb224414f2d87eef48c48291b86bca8043cc0dd692d89077b9562ac330b

Transactions (1)

Coinbase758f5eb224414f…077b9562ac330b

1 in → 1 out9.1300 XPM110 B

AeKNrjNj…1NEq95Ta

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.

8.903 × 10⁹⁸(99-digit number)

89030688033411436765…00462835261588069601

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

8.903 × 10⁹⁸(99-digit number)

89030688033411436765…00462835261588069601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.780 × 10⁹⁹(100-digit number)

17806137606682287353…00925670523176139201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.561 × 10⁹⁹(100-digit number)

35612275213364574706…01851341046352278401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.122 × 10⁹⁹(100-digit number)

71224550426729149412…03702682092704556801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.424 × 10¹⁰⁰(101-digit number)

14244910085345829882…07405364185409113601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.848 × 10¹⁰⁰(101-digit number)

28489820170691659765…14810728370818227201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.697 × 10¹⁰⁰(101-digit number)

56979640341383319530…29621456741636454401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.139 × 10¹⁰¹(102-digit number)

11395928068276663906…59242913483272908801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.279 × 10¹⁰¹(102-digit number)

22791856136553327812…18485826966545817601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.558 × 10¹⁰¹(102-digit number)

45583712273106655624…36971653933091635201

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 #474,736

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