Block #364,396

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/18/2014, 1:16:16 AM · Difficulty 10.4209 · 6,462,712 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

10a67423169afa7e7865ee2181f0883432ad324d16c2b01d2e77ac440954675c

View on Chainz ↗

Height

#364,396

Difficulty

10.420932

Transactions

Size

1.01 KB

Version

Bits

0a6bc233

Nonce

41,784

Timestamp

1/18/2014, 1:16:16 AM

Confirmations

6,462,712

Mined by

⛏️ laRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

68829a22591c31d13b59395d7dbcd4e3ed16b4197d850c51922da97d657b83fd

Transactions (1)

Coinbase68829a22591c31…2da97d657b83fd

1 in → 26 out9.1900 XPM947 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AZemWJAo…6jhDtieG Ac5JXwCr…tf5C9dQa

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.

6.410 × 10⁹⁵(96-digit number)

64108185073756448634…89113886529343398399

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

6.410 × 10⁹⁵(96-digit number)

64108185073756448634…89113886529343398399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.282 × 10⁹⁶(97-digit number)

12821637014751289726…78227773058686796799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.564 × 10⁹⁶(97-digit number)

25643274029502579453…56455546117373593599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.128 × 10⁹⁶(97-digit number)

51286548059005158907…12911092234747187199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.025 × 10⁹⁷(98-digit number)

10257309611801031781…25822184469494374399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.051 × 10⁹⁷(98-digit number)

20514619223602063563…51644368938988748799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.102 × 10⁹⁷(98-digit number)

41029238447204127126…03288737877977497599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.205 × 10⁹⁷(98-digit number)

82058476894408254252…06577475755954995199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.641 × 10⁹⁸(99-digit number)

16411695378881650850…13154951511909990399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.282 × 10⁹⁸(99-digit number)

32823390757763301700…26309903023819980799

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #364,396

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