Block #503,194

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/20/2014, 10:39:47 PM · Difficulty 10.8079 · 6,313,203 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

884507fb1f7aee8ebd6578c4060ba487481360363e74081595218642cd2d6b6f

View on Chainz ↗

Height

#503,194

Difficulty

10.807944

Transactions

Size

208 B

Version

Bits

0aced567

Nonce

428,890,707

Timestamp

4/20/2014, 10:39:47 PM

Confirmations

6,313,203

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ced99b43177cb1504d35c7e4a2003ac6c38a40dacbb1585a24ed8ba8e4173eb1

Transactions (1)

Coinbaseced99b43177cb1…ed8ba8e4173eb1

1 in → 1 out8.5500 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.

2.311 × 10¹⁰⁰(101-digit number)

23118876724770340906…35332762026162176001

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

2.311 × 10¹⁰⁰(101-digit number)

23118876724770340906…35332762026162176001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.623 × 10¹⁰⁰(101-digit number)

46237753449540681813…70665524052324352001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.247 × 10¹⁰⁰(101-digit number)

92475506899081363626…41331048104648704001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.849 × 10¹⁰¹(102-digit number)

18495101379816272725…82662096209297408001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.699 × 10¹⁰¹(102-digit number)

36990202759632545450…65324192418594816001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.398 × 10¹⁰¹(102-digit number)

73980405519265090901…30648384837189632001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.479 × 10¹⁰²(103-digit number)

14796081103853018180…61296769674379264001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.959 × 10¹⁰²(103-digit number)

29592162207706036360…22593539348758528001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.918 × 10¹⁰²(103-digit number)

59184324415412072720…45187078697517056001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.183 × 10¹⁰³(104-digit number)

11836864883082414544…90374157395034112001

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 #503,194

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