Block #483,580

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/10/2014, 3:20:27 AM · Difficulty 10.5655 · 6,332,997 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ed80a1e0f41adf663e69a21ad7915a1a7f7cbccd28cab91615afbcacf0157318

View on Chainz ↗

Height

#483,580

Difficulty

10.565500

Transactions

Size

208 B

Version

Bits

0a90c49c

Nonce

206,594,399

Timestamp

4/10/2014, 3:20:27 AM

Confirmations

6,332,997

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8e384927b74ec37cc2cf5a50e645fca3596c0ef2cdec905421ab0596b8ffe9d1

Transactions (1)

Coinbase8e384927b74ec3…ab0596b8ffe9d1

1 in → 1 out8.9400 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.

1.731 × 10¹⁰⁰(101-digit number)

17311813046871213010…25197483379874693119

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

1.731 × 10¹⁰⁰(101-digit number)

17311813046871213010…25197483379874693119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.462 × 10¹⁰⁰(101-digit number)

34623626093742426021…50394966759749386239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.924 × 10¹⁰⁰(101-digit number)

69247252187484852042…00789933519498772479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.384 × 10¹⁰¹(102-digit number)

13849450437496970408…01579867038997544959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.769 × 10¹⁰¹(102-digit number)

27698900874993940816…03159734077995089919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.539 × 10¹⁰¹(102-digit number)

55397801749987881633…06319468155990179839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.107 × 10¹⁰²(103-digit number)

11079560349997576326…12638936311980359679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.215 × 10¹⁰²(103-digit number)

22159120699995152653…25277872623960719359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.431 × 10¹⁰²(103-digit number)

44318241399990305307…50555745247921438719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.863 × 10¹⁰²(103-digit number)

88636482799980610614…01111490495842877439

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 First 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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #483,580

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