Block #62,510

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 7:48:30 PM · Difficulty 8.9766 · 6,729,895 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6f5919ba61de0a4a30fa5e8fd11deb2f508f72464b6570f34a45bb2f8921b06f

View on Chainz ↗

Height

#62,510

Difficulty

8.976560

Transactions

Size

521 B

Version

Bits

08f9ffda

Nonce

668

Timestamp

7/18/2013, 7:48:30 PM

Confirmations

6,729,895

Merkle Root

6551db7d1bdbd77dd552efebb12da6855fa2038728d655d01230ffd9e95084f7

Transactions (3)

Coinbase4bc24ad52a2c37…7cbe251115438d

1 in → 1 out12.4100 XPM110 B

AK3X8M4n…zFeMdGCF

b9a31b89ff287e…d078dc6a91f8a9

1 in → 1 out12.4300 XPM157 B

AK2Yw6fy…QfiXfRKe

5421b02282685e…089a50ed675301

1 in → 1 out12.4400 XPM157 B

AdcCq6zb…nkw452pK

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.

2.098 × 10¹¹¹(112-digit number)

20980351962652040655…28027390372012873599

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

2.098 × 10¹¹¹(112-digit number)

20980351962652040655…28027390372012873599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.196 × 10¹¹¹(112-digit number)

41960703925304081311…56054780744025747199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.392 × 10¹¹¹(112-digit number)

83921407850608162622…12109561488051494399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.678 × 10¹¹²(113-digit number)

16784281570121632524…24219122976102988799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.356 × 10¹¹²(113-digit number)

33568563140243265049…48438245952205977599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.713 × 10¹¹²(113-digit number)

67137126280486530098…96876491904411955199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.342 × 10¹¹³(114-digit number)

13427425256097306019…93752983808823910399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.685 × 10¹¹³(114-digit number)

26854850512194612039…87505967617647820799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.370 × 10¹¹³(114-digit number)

53709701024389224078…75011935235295641599

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer