Block #529,973

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/7/2014, 2:25:15 PM · Difficulty 10.8909 · 6,284,226 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

47969d372aec1f43732d57b9536ef8f222987bd9ea2dc8ec5146d98e3b6930cc

View on Chainz ↗

Height

#529,973

Difficulty

10.890910

Transactions

Size

832 B

Version

Bits

0ae412b4

Nonce

77,493

Timestamp

5/7/2014, 2:25:15 PM

Confirmations

6,284,226

Mined by

⛏️ 5xAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

818ba23c8f409d8f5a1bb694fa5b408e7095fbefac9d5519795036a06630e192

Transactions (1)

Coinbase818ba23c8f409d…5036a06630e192

1 in → 20 out8.4200 XPM743 B

AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm ASgUri65…C7NLcyBg AbHY4iza…Yckt2J5W AZr7Ptuw…CM4Yw5jq

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.

2.169 × 10⁹¹(92-digit number)

21694276780603346213…36647104865296550421

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

2.169 × 10⁹¹(92-digit number)

21694276780603346213…36647104865296550421

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.338 × 10⁹¹(92-digit number)

43388553561206692426…73294209730593100841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.677 × 10⁹¹(92-digit number)

86777107122413384852…46588419461186201681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.735 × 10⁹²(93-digit number)

17355421424482676970…93176838922372403361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.471 × 10⁹²(93-digit number)

34710842848965353940…86353677844744806721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.942 × 10⁹²(93-digit number)

69421685697930707881…72707355689489613441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.388 × 10⁹³(94-digit number)

13884337139586141576…45414711378979226881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.776 × 10⁹³(94-digit number)

27768674279172283152…90829422757958453761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.553 × 10⁹³(94-digit number)

55537348558344566305…81658845515916907521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.110 × 10⁹⁴(95-digit number)

11107469711668913261…63317691031833815041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.221 × 10⁹⁴(95-digit number)

22214939423337826522…26635382063667630081

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #529,973

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