Block #302,457

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/9/2013, 8:02:15 PM · Difficulty 9.9927 · 6,507,910 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

75b08c11b54529dc1a553a0994dbb274770476e9fa57d161ebe58bc1b2c64bbc

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Height

#302,457

Difficulty

9.992722

Transactions

Size

1.08 KB

Version

Bits

09fe230a

Nonce

187,353

Timestamp

12/9/2013, 8:02:15 PM

Confirmations

6,507,910

Mined by

⛏️ yaR!JAHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

6f05818bc43e081dcf46f1fab2903a1e0726c9ec8cede905be7d8b795dbdfd74

Transactions (1)

Coinbase6f05818bc43e08…7d8b795dbdfd74

1 in → 28 out9.9800 XPM1015 B

AHuJ9wYh…BGmgHrKZ Ad9pSzHt…cpJ3y2zz AYtDvcGs…VuAcA7m7 AUFxANzC…wSxXZx69 AYqpXoh8…kHurq7wG

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.

3.138 × 10⁸⁹(90-digit number)

31386510409270146065…22221159859274005761

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

3.138 × 10⁸⁹(90-digit number)

31386510409270146065…22221159859274005761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.277 × 10⁸⁹(90-digit number)

62773020818540292130…44442319718548011521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.255 × 10⁹⁰(91-digit number)

12554604163708058426…88884639437096023041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.510 × 10⁹⁰(91-digit number)

25109208327416116852…77769278874192046081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.021 × 10⁹⁰(91-digit number)

50218416654832233704…55538557748384092161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.004 × 10⁹¹(92-digit number)

10043683330966446740…11077115496768184321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.008 × 10⁹¹(92-digit number)

20087366661932893481…22154230993536368641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.017 × 10⁹¹(92-digit number)

40174733323865786963…44308461987072737281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.034 × 10⁹¹(92-digit number)

80349466647731573926…88616923974145474561

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

Block #302,457

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