Block #75,757

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/21/2013, 6:37:06 PM · Difficulty 9.0391 · 6,731,848 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ace0c6c86a38fbc879cf48dfcbb1a519494060fe847a6e5ec65c055272151dd7

View on Chainz ↗

Height

#75,757

Difficulty

9.039147

Transactions

Size

1.05 KB

Version

Bits

090a058f

Nonce

1,736

Timestamp

7/21/2013, 6:37:06 PM

Confirmations

6,731,848

Mined by

⛏️ P2SHAVQxbFsH6aZpX2pFKM69EEQVEFKG2vYXbz

Merkle Root

160b4a0030398b71c9829a12c2d756dab3cb214f0e11337ebe0681d36ec23818

Transactions (3)

Coinbase652d92e37a8654…9a6d9e662b5e4e

1 in → 1 out12.2400 XPM110 B

AVQxbFsH…KG2vYXbz

cfb628ee451cf8…bb0d3aa2475314

3 in → 2 out329.3351 XPM522 B

AXMHnTJs…gn5QCAnT AUcPYpR8…GsdhhWgo

6a4e6e338d69ec…07e9775640e43b

2 in → 1 out74.0000 XPM341 B

AJV9J7t5…G9F5PrK8

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.

1.447 × 10¹²⁹(130-digit number)

14470201648320677530…26501284065182467359

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

1.447 × 10¹²⁹(130-digit number)

14470201648320677530…26501284065182467359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.894 × 10¹²⁹(130-digit number)

28940403296641355061…53002568130364934719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.788 × 10¹²⁹(130-digit number)

57880806593282710123…06005136260729869439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.157 × 10¹³⁰(131-digit number)

11576161318656542024…12010272521459738879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.315 × 10¹³⁰(131-digit number)

23152322637313084049…24020545042919477759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.630 × 10¹³⁰(131-digit number)

46304645274626168098…48041090085838955519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.260 × 10¹³⁰(131-digit number)

92609290549252336197…96082180171677911039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.852 × 10¹³¹(132-digit number)

18521858109850467239…92164360343355822079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.704 × 10¹³¹(132-digit number)

37043716219700934478…84328720686711644159

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 #75,757

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