Block #290,795

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/2/2013, 8:57:07 PM · Difficulty 9.9895 · 6,508,548 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b28d78ffbed975f7b9a27e2992bca7b350c436b24b34dbba0a5c56f470869342

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Height

#290,795

Difficulty

9.989459

Transactions

Size

1.15 KB

Version

Bits

09fd4d2b

Nonce

135,640

Timestamp

12/2/2013, 8:57:07 PM

Confirmations

6,508,548

Mined by

⛏️ oaRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

19c1831a21ff48dfdc31629cfe3cd25d895176509d04637755a651a3f6133136

Transactions (1)

Coinbase19c1831a21ff48…a651a3f6133136

1 in → 30 out9.9900 XPM1.06 KB

AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz AbUZ8W5N…wEAzXuVd ASD5y7K3…PadKp2tW AFtwoVbg…MRC1TUur

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.

9.312 × 10¹⁰⁰(101-digit number)

93128707097744218778…59078850905607310721

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

9.312 × 10¹⁰⁰(101-digit number)

93128707097744218778…59078850905607310721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.862 × 10¹⁰¹(102-digit number)

18625741419548843755…18157701811214621441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.725 × 10¹⁰¹(102-digit number)

37251482839097687511…36315403622429242881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.450 × 10¹⁰¹(102-digit number)

74502965678195375022…72630807244858485761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.490 × 10¹⁰²(103-digit number)

14900593135639075004…45261614489716971521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.980 × 10¹⁰²(103-digit number)

29801186271278150009…90523228979433943041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.960 × 10¹⁰²(103-digit number)

59602372542556300018…81046457958867886081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.192 × 10¹⁰³(104-digit number)

11920474508511260003…62092915917735772161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.384 × 10¹⁰³(104-digit number)

23840949017022520007…24185831835471544321

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