Block #291,011

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/2/2013, 11:31:46 PM · Difficulty 9.9896 · 6,505,055 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5527db60646ac34c468f0408f8f52bc6c46adbb5d3fdb5055acc704815e298dc

View on Chainz ↗

Height

#291,011

Difficulty

9.989595

Transactions

Size

1.05 KB

Version

Bits

09fd561f

Nonce

92,546

Timestamp

12/2/2013, 11:31:46 PM

Confirmations

6,505,055

Mined by

⛏️ paR0AZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

84810cb0afbf77cb8b8ec17508670356322edca059547d95301109d1190d7692

Transactions (1)

Coinbase84810cb0afbf77…1109d1190d7692

1 in → 27 out10.0100 XPM981 B

AZninDSu…FvgDMwC4 AZ3bZpff…LnRQBGfh AWGQhzDN…RDYvugUy AYcLTeXR…bscgPops ASWp6454…JFPEKgqq

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.

4.189 × 10⁹⁷(98-digit number)

41893514004300926448…07265735080925818881

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

4.189 × 10⁹⁷(98-digit number)

41893514004300926448…07265735080925818881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.378 × 10⁹⁷(98-digit number)

83787028008601852896…14531470161851637761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.675 × 10⁹⁸(99-digit number)

16757405601720370579…29062940323703275521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.351 × 10⁹⁸(99-digit number)

33514811203440741158…58125880647406551041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.702 × 10⁹⁸(99-digit number)

67029622406881482317…16251761294813102081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.340 × 10⁹⁹(100-digit number)

13405924481376296463…32503522589626204161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.681 × 10⁹⁹(100-digit number)

26811848962752592926…65007045179252408321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.362 × 10⁹⁹(100-digit number)

53623697925505185853…30014090358504816641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.072 × 10¹⁰⁰(101-digit number)

10724739585101037170…60028180717009633281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.144 × 10¹⁰⁰(101-digit number)

21449479170202074341…20056361434019266561

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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