Block #77,687

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2013, 12:25:08 PM · Difficulty 9.1915 · 6,728,933 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

796cc9cfd690b8373d9e71d37f7ce2ebca544e5716cf0ab548f4734b8cd73e79

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Height

#77,687

Difficulty

9.191543

Transactions

Size

208 B

Version

Bits

093108fc

Nonce

2,318

Timestamp

7/22/2013, 12:25:08 PM

Confirmations

6,728,933

Mined by

⛏️ P2SHAGCUbq6Mxc7yQk3kiL3txXdSCgQSxWg1oL

Merkle Root

c631fb9b9701c8890830a1d65ea7279dddf6c61ee12fb302297051fb01ed9ce2

Transactions (1)

Coinbasec631fb9b9701c8…7051fb01ed9ce2

1 in → 1 out11.8200 XPM110 B

AGCUbq6M…QSxWg1oL

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.

3.567 × 10¹¹⁴(115-digit number)

35672811406763414896…80587616807694974351

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

3.567 × 10¹¹⁴(115-digit number)

35672811406763414896…80587616807694974351

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.134 × 10¹¹⁴(115-digit number)

71345622813526829792…61175233615389948701

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.426 × 10¹¹⁵(116-digit number)

14269124562705365958…22350467230779897401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.853 × 10¹¹⁵(116-digit number)

28538249125410731917…44700934461559794801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.707 × 10¹¹⁵(116-digit number)

57076498250821463834…89401868923119589601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.141 × 10¹¹⁶(117-digit number)

11415299650164292766…78803737846239179201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.283 × 10¹¹⁶(117-digit number)

22830599300328585533…57607475692478358401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.566 × 10¹¹⁶(117-digit number)

45661198600657171067…15214951384956716801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.132 × 10¹¹⁶(117-digit number)

91322397201314342134…30429902769913433601

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 #77,687

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