Block #252,668

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/9/2013, 5:10:15 PM · Difficulty 9.9714 · 6,538,275 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

01c3b64d523f5aebfa771f82b59054b4fdd12d6a13fddff8e7483190ae27a642

View on Chainz ↗

Height

#252,668

Difficulty

9.971368

Transactions

Size

2.11 KB

Version

Bits

09f8ab92

Nonce

8,623

Timestamp

11/9/2013, 5:10:15 PM

Confirmations

6,538,275

Merkle Root

c9c061a69e34fca9860e642b80c8ccf6b7cd974e80325858564d39b634d686b7

Transactions (2)

Coinbase4fceeabe5a91e0…f596223110dedb

1 in → 35 out10.0200 XPM1.22 KB

AQtzUSwq…htAuF3yC AHkgKuuD…TkWqWiw1 AVbjNLpc…e1xsNhVz ARQrJViM…5cGXU5z4 AJaGRnaj…iCHGoy6E

b1b20ab69f5fda…0b010fa6a9dfd4

5 in → 2 out0.0415 XPM819 B

AJtCDakk…cmy9cKRa AGbTSZLY…f6unLNcs

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.

2.963 × 10⁸⁸(89-digit number)

29638463192535870616…80951446886877680241

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

2.963 × 10⁸⁸(89-digit number)

29638463192535870616…80951446886877680241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.927 × 10⁸⁸(89-digit number)

59276926385071741233…61902893773755360481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.185 × 10⁸⁹(90-digit number)

11855385277014348246…23805787547510720961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.371 × 10⁸⁹(90-digit number)

23710770554028696493…47611575095021441921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.742 × 10⁸⁹(90-digit number)

47421541108057392986…95223150190042883841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.484 × 10⁸⁹(90-digit number)

94843082216114785973…90446300380085767681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.896 × 10⁹⁰(91-digit number)

18968616443222957194…80892600760171535361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.793 × 10⁹⁰(91-digit number)

37937232886445914389…61785201520343070721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.587 × 10⁹⁰(91-digit number)

75874465772891828778…23570403040686141441

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