Block #303,394

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/10/2013, 8:47:30 AM · Difficulty 9.9930 · 6,506,166 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

df3e02535088712b1e1203d631001e1d389254e62c926deed01230a967931acd

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Height

#303,394

Difficulty

9.992993

Transactions

Size

966 B

Version

Bits

09fe34ca

Nonce

136,188

Timestamp

12/10/2013, 8:47:30 AM

Confirmations

6,506,166

Mined by

⛏️ "aR'AJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

45b3ba4d6e25d3a884e53722995ec8a83744819b2b10ab6898fb5bd06b1c9cab

Transactions (1)

Coinbase45b3ba4d6e25d3…fb5bd06b1c9cab

1 in → 24 out10.0000 XPM878 B

AJzWx2VD…j4ZSMit5 AdV5u966…MgezYDKc AQyr8Lw3…hs4nt3Pn Ad9pSzHt…cpJ3y2zz ASy2XdSN…okx2X1HY

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.

7.864 × 10⁸⁹(90-digit number)

78645875845349856981…52593384745281947681

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

7.864 × 10⁸⁹(90-digit number)

78645875845349856981…52593384745281947681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.572 × 10⁹⁰(91-digit number)

15729175169069971396…05186769490563895361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.145 × 10⁹⁰(91-digit number)

31458350338139942792…10373538981127790721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.291 × 10⁹⁰(91-digit number)

62916700676279885585…20747077962255581441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.258 × 10⁹¹(92-digit number)

12583340135255977117…41494155924511162881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.516 × 10⁹¹(92-digit number)

25166680270511954234…82988311849022325761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.033 × 10⁹¹(92-digit number)

50333360541023908468…65976623698044651521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.006 × 10⁹²(93-digit number)

10066672108204781693…31953247396089303041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.013 × 10⁹²(93-digit number)

20133344216409563387…63906494792178606081

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 #303,394

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