Block #61,996

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 4:32:03 PM · Difficulty 8.9750 · 6,729,717 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4d288b9e19a9e862be76a9d1a7820976835f8952946d091e3b8da12442284b95

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Height

#61,996

Difficulty

8.975019

Transactions

Size

1.22 KB

Version

Bits

08f99ade

Nonce

640

Timestamp

7/18/2013, 4:32:03 PM

Confirmations

6,729,717

Merkle Root

0d25d7a26b4ed741868dd8100ed1c4ec258ce21391c0f5f60ab30c83c3a732f0

Transactions (3)

Coinbase2494d9ee942adc…f84af331a3cc57

1 in → 1 out12.4200 XPM109 B

AK1JUKWL…oPR4rN5o

98c7a075df61ae…f731dd64d6ebd9

4 in → 2 out388.9540 XPM669 B

AWqZEKXc…EP6pgWVR AJN5CRTA…YDuZ9ysd

54be231edb7bb6…ddb4bba34d2cd9

2 in → 2 out17.6900 XPM374 B

AL7jLiZf…77a9nPT4 AWCpn94W…AVCFuzza

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.

4.477 × 10¹¹³(114-digit number)

44779620310905630926…28603590234862998471

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

4.477 × 10¹¹³(114-digit number)

44779620310905630926…28603590234862998471

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.955 × 10¹¹³(114-digit number)

89559240621811261852…57207180469725996941

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.791 × 10¹¹⁴(115-digit number)

17911848124362252370…14414360939451993881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.582 × 10¹¹⁴(115-digit number)

35823696248724504741…28828721878903987761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.164 × 10¹¹⁴(115-digit number)

71647392497449009482…57657443757807975521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.432 × 10¹¹⁵(116-digit number)

14329478499489801896…15314887515615951041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.865 × 10¹¹⁵(116-digit number)

28658956998979603792…30629775031231902081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.731 × 10¹¹⁵(116-digit number)

57317913997959207585…61259550062463804161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.146 × 10¹¹⁶(117-digit number)

11463582799591841517…22519100124927608321

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