Block #76,521

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2013, 1:26:34 AM · Difficulty 9.1047 · 6,713,604 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ec62b1336c6dcf9e0660d8146b92a5f533cc6cf8e586e86de14763299cd45820

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Height

#76,521

Difficulty

9.104740

Transactions

Size

205 B

Version

Bits

091ad043

Nonce

Timestamp

7/22/2013, 1:26:34 AM

Confirmations

6,713,604

Merkle Root

d5c19dcd7abfe25add2d13bb329c7e67fae51a62236145f066d46ae5f37f20d4

Transactions (1)

Coinbased5c19dcd7abfe2…d46ae5f37f20d4

1 in → 1 out12.0500 XPM110 B

AcBadmkp…GmhL921o

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.

1.464 × 10¹⁰⁷(108-digit number)

14649902709567725606…37792868368151996481

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

1.464 × 10¹⁰⁷(108-digit number)

14649902709567725606…37792868368151996481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.929 × 10¹⁰⁷(108-digit number)

29299805419135451213…75585736736303992961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.859 × 10¹⁰⁷(108-digit number)

58599610838270902426…51171473472607985921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.171 × 10¹⁰⁸(109-digit number)

11719922167654180485…02342946945215971841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.343 × 10¹⁰⁸(109-digit number)

23439844335308360970…04685893890431943681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.687 × 10¹⁰⁸(109-digit number)

46879688670616721941…09371787780863887361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.375 × 10¹⁰⁸(109-digit number)

93759377341233443882…18743575561727774721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.875 × 10¹⁰⁹(110-digit number)

18751875468246688776…37487151123455549441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.750 × 10¹⁰⁹(110-digit number)

37503750936493377553…74974302246911098881

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer