Block #91,809

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/1/2013, 6:06:50 AM · Difficulty 9.2075 · 6,703,289 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a1f11c14e5fbdc8cc50cc978e4d630950b5ce4ecb4d64570f6dd766c640980e2

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Height

#91,809

Difficulty

9.207542

Transactions

Size

205 B

Version

Bits

09352172

Nonce

28,639

Timestamp

8/1/2013, 6:06:50 AM

Confirmations

6,703,289

Mined by

⛏️ P2SHAdZa3TAmYfw2F4ATA4X4uw6uWdcTySUJQt

Merkle Root

1b72454ee6987f729f02da3c52fcd7a1038748907d5239d9e42deb3c823b9a36

Transactions (1)

Coinbase1b72454ee6987f…2deb3c823b9a36

1 in → 1 out11.7800 XPM109 B

AdZa3TAm…cTySUJQt

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.

7.872 × 10¹⁰⁸(109-digit number)

78726088556133897686…85532779810313490051

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

7.872 × 10¹⁰⁸(109-digit number)

78726088556133897686…85532779810313490051

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.574 × 10¹⁰⁹(110-digit number)

15745217711226779537…71065559620626980101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.149 × 10¹⁰⁹(110-digit number)

31490435422453559074…42131119241253960201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.298 × 10¹⁰⁹(110-digit number)

62980870844907118148…84262238482507920401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.259 × 10¹¹⁰(111-digit number)

12596174168981423629…68524476965015840801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.519 × 10¹¹⁰(111-digit number)

25192348337962847259…37048953930031681601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.038 × 10¹¹⁰(111-digit number)

50384696675925694519…74097907860063363201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.007 × 10¹¹¹(112-digit number)

10076939335185138903…48195815720126726401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.015 × 10¹¹¹(112-digit number)

20153878670370277807…96391631440253452801

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