Block #87,117

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/28/2013, 3:44:30 PM · Difficulty 9.2808 · 6,706,452 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7d6f70c0c96ba92a5f547b289dffa0c34c381248d00d6d88e2f346a057340cf0

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Height

#87,117

Difficulty

9.280769

Transactions

Size

204 B

Version

Bits

0947e07a

Nonce

50,294

Timestamp

7/28/2013, 3:44:30 PM

Confirmations

6,706,452

Merkle Root

307b64968aabbe2fcf382c5b7cd863cbd576734b8958f65ed98e6ee70359ed86

Transactions (1)

Coinbase307b64968aabbe…8e6ee70359ed86

1 in → 1 out11.5900 XPM109 B

ASXW8s4r…LM8vqY9U

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.

1.856 × 10¹⁰⁷(108-digit number)

18563534815250619276…12289036069290845321

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

1.856 × 10¹⁰⁷(108-digit number)

18563534815250619276…12289036069290845321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.712 × 10¹⁰⁷(108-digit number)

37127069630501238552…24578072138581690641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.425 × 10¹⁰⁷(108-digit number)

74254139261002477104…49156144277163381281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.485 × 10¹⁰⁸(109-digit number)

14850827852200495420…98312288554326762561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.970 × 10¹⁰⁸(109-digit number)

29701655704400990841…96624577108653525121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.940 × 10¹⁰⁸(109-digit number)

59403311408801981683…93249154217307050241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.188 × 10¹⁰⁹(110-digit number)

11880662281760396336…86498308434614100481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.376 × 10¹⁰⁹(110-digit number)

23761324563520792673…72996616869228200961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.752 × 10¹⁰⁹(110-digit number)

47522649127041585346…45993233738456401921

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