Block #294,952

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 12/5/2013, 4:28:27 AM · Difficulty 9.9912 · 6,502,914 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

88db669cec627149fe2166b8a21616b9b6dedaee5d6379a1fb926b1371a6693e

View on Chainz ↗

Height

#294,952

Difficulty

9.991177

Transactions

Size

1.15 KB

Version

Bits

09fdbdcf

Nonce

88,332

Timestamp

12/5/2013, 4:28:27 AM

Confirmations

6,502,914

Mined by

⛏️ aRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

45aeecce972d945165c5026a5d75986577093d4568b9cf98aea308a33598f956

Transactions (1)

Coinbase45aeecce972d94…a308a33598f956

1 in → 30 out9.9800 XPM1.06 KB

AYcLTeXR…bscgPops ASXEwJrb…E3MLWChF AJHH6QuE…N3s6fxLC Aew3LURi…RX2atbvx AKwqFUdz…D4jGNKFN

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.

1.916 × 10¹⁰⁸(109-digit number)

19165649710230625530…20560611681770311039

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

1.916 × 10¹⁰⁸(109-digit number)

19165649710230625530…20560611681770311039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.833 × 10¹⁰⁸(109-digit number)

38331299420461251060…41121223363540622079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.666 × 10¹⁰⁸(109-digit number)

76662598840922502120…82242446727081244159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.533 × 10¹⁰⁹(110-digit number)

15332519768184500424…64484893454162488319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.066 × 10¹⁰⁹(110-digit number)

30665039536369000848…28969786908324976639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.133 × 10¹⁰⁹(110-digit number)

61330079072738001696…57939573816649953279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.226 × 10¹¹⁰(111-digit number)

12266015814547600339…15879147633299906559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.453 × 10¹¹⁰(111-digit number)

24532031629095200678…31758295266599813119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.906 × 10¹¹⁰(111-digit number)

49064063258190401357…63516590533199626239

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer