Block #506,814

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/23/2014, 8:06:01 AM · Difficulty 10.8149 · 6,310,370 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4954a1bf7e788b6b3f835b452b349525a5e156004595b73edde9f73b397276f0

View on Chainz ↗

Height

#506,814

Difficulty

10.814912

Transactions

Size

208 B

Version

Bits

0ad09e0d

Nonce

22,209,126

Timestamp

4/23/2014, 8:06:01 AM

Confirmations

6,310,370

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

2faf2a2e6bbfe26a4cf8fd7b0b386154f350263fe2b0216e98419fd338bdcd63

Transactions (1)

Coinbase2faf2a2e6bbfe2…419fd338bdcd63

1 in → 1 out8.5400 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.

1.726 × 10¹⁰⁰(101-digit number)

17260119622418651966…41849501426724948479

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

1.726 × 10¹⁰⁰(101-digit number)

17260119622418651966…41849501426724948479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.452 × 10¹⁰⁰(101-digit number)

34520239244837303933…83699002853449896959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.904 × 10¹⁰⁰(101-digit number)

69040478489674607866…67398005706899793919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.380 × 10¹⁰¹(102-digit number)

13808095697934921573…34796011413799587839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.761 × 10¹⁰¹(102-digit number)

27616191395869843146…69592022827599175679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.523 × 10¹⁰¹(102-digit number)

55232382791739686293…39184045655198351359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.104 × 10¹⁰²(103-digit number)

11046476558347937258…78368091310396702719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.209 × 10¹⁰²(103-digit number)

22092953116695874517…56736182620793405439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.418 × 10¹⁰²(103-digit number)

44185906233391749034…13472365241586810879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.837 × 10¹⁰²(103-digit number)

88371812466783498069…26944730483173621759

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 #506,814

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