Block #300,235

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/8/2013, 11:46:18 AM · Difficulty 9.9922 · 6,508,196 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2cd43248346e01adae1674b106d898c374d3579882ab320d048d41c5ae3c1441

View on Chainz ↗

Height

#300,235

Difficulty

9.992222

Transactions

Size

1.08 KB

Version

Bits

09fe0240

Nonce

18,738

Timestamp

12/8/2013, 11:46:18 AM

Confirmations

6,508,196

Mined by

⛏️ aRAe6gEbs5i5LrBXcGb93Lduqktkm5Mn8oYw

Merkle Root

c28a8180e787aea9364a4140ef7a68910212cfa13a0aba85febbf8ba4a806eaf

Transactions (1)

Coinbasec28a8180e787ae…bbf8ba4a806eaf

1 in → 28 out9.9800 XPM1015 B

Ae6gEbs5…m5Mn8oYw AaJwNkvB…uqCwyjYa AYcLTeXR…bscgPops AN9op6p8…UkEq2gcy AKCfzALy…4mCD8qcV

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.

2.631 × 10⁹³(94-digit number)

26317952703509569295…87635029501268754779

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

2.631 × 10⁹³(94-digit number)

26317952703509569295…87635029501268754779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.263 × 10⁹³(94-digit number)

52635905407019138591…75270059002537509559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.052 × 10⁹⁴(95-digit number)

10527181081403827718…50540118005075019119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.105 × 10⁹⁴(95-digit number)

21054362162807655436…01080236010150038239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.210 × 10⁹⁴(95-digit number)

42108724325615310873…02160472020300076479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.421 × 10⁹⁴(95-digit number)

84217448651230621746…04320944040600152959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.684 × 10⁹⁵(96-digit number)

16843489730246124349…08641888081200305919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.368 × 10⁹⁵(96-digit number)

33686979460492248698…17283776162400611839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.737 × 10⁹⁵(96-digit number)

67373958920984497397…34567552324801223679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.347 × 10⁹⁶(97-digit number)

13474791784196899479…69135104649602447359

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 #300,235

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