Block #365,963

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/19/2014, 2:52:11 AM · Difficulty 10.4252 · 6,439,237 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

79e54fee97e1ae9f81381e250c88a544541ab26ffe9e052b8db5567425cb54ea

View on Chainz ↗

Height

#365,963

Difficulty

10.425223

Transactions

Size

1.01 KB

Version

Bits

0a6cdb70

Nonce

104,232

Timestamp

1/19/2014, 2:52:11 AM

Confirmations

6,439,237

Mined by

⛏️ aR=Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

ddaf0c06fdecf52842b40fe501eaf909ec9cd88aa128e7399ac9ccbd04d39f55

Transactions (1)

Coinbaseddaf0c06fdecf5…c9ccbd04d39f55

1 in → 26 out9.1900 XPM947 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AKR19pvT…zWLSNpj7 AQwRN8bE…V8PsTcY9

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.

9.355 × 10⁹⁷(98-digit number)

93552199431083474310…56794133437273501499

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

9.355 × 10⁹⁷(98-digit number)

93552199431083474310…56794133437273501499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.871 × 10⁹⁸(99-digit number)

18710439886216694862…13588266874547002999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.742 × 10⁹⁸(99-digit number)

37420879772433389724…27176533749094005999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.484 × 10⁹⁸(99-digit number)

74841759544866779448…54353067498188011999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.496 × 10⁹⁹(100-digit number)

14968351908973355889…08706134996376023999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.993 × 10⁹⁹(100-digit number)

29936703817946711779…17412269992752047999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.987 × 10⁹⁹(100-digit number)

59873407635893423558…34824539985504095999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.197 × 10¹⁰⁰(101-digit number)

11974681527178684711…69649079971008191999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.394 × 10¹⁰⁰(101-digit number)

23949363054357369423…39298159942016383999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.789 × 10¹⁰⁰(101-digit number)

47898726108714738846…78596319884032767999

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