Block #88,054

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/29/2013, 8:12:08 AM · Difficulty 9.2739 · 6,701,738 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b21283b0036461863abbaf5d2773b9ae84c6008b2aada231fd3ff7b7fe37a76c

View on Chainz ↗

Height

#88,054

Difficulty

9.273917

Transactions

Size

20.54 KB

Version

Bits

09461f67

Nonce

552

Timestamp

7/29/2013, 8:12:08 AM

Confirmations

6,701,738

Merkle Root

4a2dc0f24a768c8517b53baeeb37e47d0f1ca59ccab1472158c93bd91609433d

Transactions (4)

Coinbase2681e26f02ebca…9660c4fa4ddcbe

1 in → 1 out11.8300 XPM110 B

AT3Bb7c7…rCC2CsmN

37d725c384db37…7aed97c06535bf

172 in → 2 out2001.2600 XPM19.22 KB

Ad4kL7ba…bcxscyCR AMRPjem1…D1yXeBX6

f632677be059fa…8a53c039a2b9bb

1 in → 2 out11.6200 XPM192 B

AKUcfpDd…aSdrQxaw AVWm17kg…NLX81xfd

390eb65c3cd5fd…43025a8df62a26

6 in → 2 out155.6337 XPM965 B

Af1a9cyi…9WPaqsSS AKERrhLz…A2qc9iWL

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.

2.859 × 10⁸⁸(89-digit number)

28591300508141359308…29573010676049704001

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

2.859 × 10⁸⁸(89-digit number)

28591300508141359308…29573010676049704001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.718 × 10⁸⁸(89-digit number)

57182601016282718616…59146021352099408001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.143 × 10⁸⁹(90-digit number)

11436520203256543723…18292042704198816001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.287 × 10⁸⁹(90-digit number)

22873040406513087446…36584085408397632001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.574 × 10⁸⁹(90-digit number)

45746080813026174893…73168170816795264001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.149 × 10⁸⁹(90-digit number)

91492161626052349786…46336341633590528001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.829 × 10⁹⁰(91-digit number)

18298432325210469957…92672683267181056001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.659 × 10⁹⁰(91-digit number)

36596864650420939914…85345366534362112001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.319 × 10⁹⁰(91-digit number)

73193729300841879829…70690733068724224001

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