Block #87,664

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 2:02:21 AM · Difficulty 9.2708 · 6,719,565 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

dbb2ffc23bc9e52cc1c67924a4d54b7e7232a1f40134df72e3f91ca5118a3c52

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Height

#87,664

Difficulty

9.270838

Transactions

Size

206 B

Version

Bits

094555aa

Nonce

258,219

Timestamp

7/29/2013, 2:02:21 AM

Confirmations

6,719,565

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

7be24e5539103e28d03ec6a4ff1943649610eca0a303976fc72082573d3b3b27

Transactions (1)

Coinbase7be24e5539103e…2082573d3b3b27

1 in → 1 out11.6200 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.

4.410 × 10¹¹²(113-digit number)

44102036013308358469…47937012737555410001

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

4.410 × 10¹¹²(113-digit number)

44102036013308358469…47937012737555410001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.820 × 10¹¹²(113-digit number)

88204072026616716939…95874025475110820001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.764 × 10¹¹³(114-digit number)

17640814405323343387…91748050950221640001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.528 × 10¹¹³(114-digit number)

35281628810646686775…83496101900443280001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.056 × 10¹¹³(114-digit number)

70563257621293373551…66992203800886560001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.411 × 10¹¹⁴(115-digit number)

14112651524258674710…33984407601773120001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.822 × 10¹¹⁴(115-digit number)

28225303048517349420…67968815203546240001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.645 × 10¹¹⁴(115-digit number)

56450606097034698841…35937630407092480001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.129 × 10¹¹⁵(116-digit number)

11290121219406939768…71875260814184960001

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 #87,664

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