Block #290,102

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/2/2013, 12:39:56 PM · Difficulty 9.9890 · 6,505,816 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

020df5619682f657901e78a8f2bff35e90429ae5871a1176a5fa76f20f1bceeb

View on Chainz ↗

Height

#290,102

Difficulty

9.988993

Transactions

Size

1.11 KB

Version

Bits

09fd2ead

Nonce

125,145

Timestamp

12/2/2013, 12:39:56 PM

Confirmations

6,505,816

Mined by

⛏️ 6maR|SAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

4a0cfb8bca4cc3e727e617b2407d57ceec6b616f6a30afcc931d573c1effd5ba

Transactions (1)

Coinbase4a0cfb8bca4cc3…1d573c1effd5ba

1 in → 29 out9.9839 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz APzYcXfB…4vHLVzHf AUW89vJd…BiczGLRw AZ2pPuKg…95SN2Yr7 AQwd2tMy…CzytqW6x

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.

1.015 × 10⁹³(94-digit number)

10157789089765353311…31127909723203425601

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

1.015 × 10⁹³(94-digit number)

10157789089765353311…31127909723203425601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.031 × 10⁹³(94-digit number)

20315578179530706623…62255819446406851201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.063 × 10⁹³(94-digit number)

40631156359061413247…24511638892813702401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.126 × 10⁹³(94-digit number)

81262312718122826494…49023277785627404801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.625 × 10⁹⁴(95-digit number)

16252462543624565298…98046555571254809601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.250 × 10⁹⁴(95-digit number)

32504925087249130597…96093111142509619201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.500 × 10⁹⁴(95-digit number)

65009850174498261195…92186222285019238401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.300 × 10⁹⁵(96-digit number)

13001970034899652239…84372444570038476801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.600 × 10⁹⁵(96-digit number)

26003940069799304478…68744889140076953601

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