Block #271,797

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/24/2013, 8:21:07 PM · Difficulty 9.9525 · 6,538,800 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3b11788fc2e64d860627a8400812ad71a0f12ff7d3488a971bc49de3a67d97ba

View on Chainz ↗

Height

#271,797

Difficulty

9.952465

Transactions

Size

1.11 KB

Version

Bits

09f3d4b9

Nonce

33,651

Timestamp

11/24/2013, 8:21:07 PM

Confirmations

6,538,800

Mined by

⛏️ %aR_Ac5sZcdPRNjfrTK9pchLQrJN4XkzV4eckG

Merkle Root

c7d342a6cdfe8c8610c70f72bcb4299484d8826d954c0293e84c89ee1bc08349

Transactions (1)

Coinbasec7d342a6cdfe8c…4c89ee1bc08349

1 in → 29 out10.0600 XPM1.02 KB

Ac5sZcdP…kzV4eckG AQyr8Lw3…hs4nt3Pn AUSGA5VC…GYHbnJtz ALdHh27b…XNbqrvPf AMbCuLHZ…WSoStwkc

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.

1.861 × 10⁹²(93-digit number)

18612416919305569152…66392814375248828959

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

1.861 × 10⁹²(93-digit number)

18612416919305569152…66392814375248828959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.722 × 10⁹²(93-digit number)

37224833838611138304…32785628750497657919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.444 × 10⁹²(93-digit number)

74449667677222276608…65571257500995315839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.488 × 10⁹³(94-digit number)

14889933535444455321…31142515001990631679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.977 × 10⁹³(94-digit number)

29779867070888910643…62285030003981263359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.955 × 10⁹³(94-digit number)

59559734141777821286…24570060007962526719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.191 × 10⁹⁴(95-digit number)

11911946828355564257…49140120015925053439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.382 × 10⁹⁴(95-digit number)

23823893656711128514…98280240031850106879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.764 × 10⁹⁴(95-digit number)

47647787313422257029…96560480063700213759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #271,797

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