Block #86,193

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/27/2013, 11:11:27 PM · Difficulty 9.2907 · 6,708,538 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6c5227b94a73f7859201d9f4a6b377c4bc9f0a27731f37af6844317b68c9a9e2

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Height

#86,193

Difficulty

9.290713

Transactions

Size

213 B

Version

Bits

094a6c23

Nonce

74,974

Timestamp

7/27/2013, 11:11:27 PM

Confirmations

6,708,538

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

11a4ea676135fbf0ca27482267b2b3da6bc9247f6a530dd3ccf1aaf0a2342952

Transactions (1)

Coinbase11a4ea676135fb…f1aaf0a2342952

1 in → 1 out11.5700 XPM109 B

AcuJraLT…Y66BS47Q

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.

2.809 × 10¹²⁷(128-digit number)

28091487315985942482…16381356507819463771

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

2.809 × 10¹²⁷(128-digit number)

28091487315985942482…16381356507819463771

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.618 × 10¹²⁷(128-digit number)

56182974631971884965…32762713015638927541

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.123 × 10¹²⁸(129-digit number)

11236594926394376993…65525426031277855081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.247 × 10¹²⁸(129-digit number)

22473189852788753986…31050852062555710161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.494 × 10¹²⁸(129-digit number)

44946379705577507972…62101704125111420321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.989 × 10¹²⁸(129-digit number)

89892759411155015944…24203408250222840641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.797 × 10¹²⁹(130-digit number)

17978551882231003188…48406816500445681281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.595 × 10¹²⁹(130-digit number)

35957103764462006377…96813633000891362561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.191 × 10¹²⁹(130-digit number)

71914207528924012755…93627266001782725121

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