Block #77,588

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2013, 11:36:52 AM · Difficulty 9.1825 · 6,740,012 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

89005086c94ec2a8d3910ca1cb26b787de39c57386bdb8eb5d3b96c5038fa91b

View on Chainz ↗

Height

#77,588

Difficulty

9.182456

Transactions

Size

363 B

Version

Bits

092eb56e

Nonce

161

Timestamp

7/22/2013, 11:36:52 AM

Confirmations

6,740,012

Mined by

⛏️ P2SHAZN8UG3e8hg6T4a3ParzrmbAeDToHEix8n

Merkle Root

d5d6469b6f3399a85fefd1302713d0d70fe129d1ffa3e4a1ed31dea7ad6c0779

Transactions (2)

Coinbase793bbf29de963a…5a8b418663358b

1 in → 1 out11.8500 XPM110 B

AZN8UG3e…ToHEix8n

f5b7167b525315…ddfecc08724343

1 in → 1 out12.3300 XPM157 B

APMGbH5f…JG5Qga2G

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.

1.749 × 10¹¹⁰(111-digit number)

17494244348515294119…32062313281459917531

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

1.749 × 10¹¹⁰(111-digit number)

17494244348515294119…32062313281459917531

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.498 × 10¹¹⁰(111-digit number)

34988488697030588238…64124626562919835061

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.997 × 10¹¹⁰(111-digit number)

69976977394061176477…28249253125839670121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.399 × 10¹¹¹(112-digit number)

13995395478812235295…56498506251679340241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.799 × 10¹¹¹(112-digit number)

27990790957624470590…12997012503358680481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.598 × 10¹¹¹(112-digit number)

55981581915248941181…25994025006717360961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.119 × 10¹¹²(113-digit number)

11196316383049788236…51988050013434721921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.239 × 10¹¹²(113-digit number)

22392632766099576472…03976100026869443841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.478 × 10¹¹²(113-digit number)

44785265532199152945…07952200053738887681

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

Block #77,588

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