Block #248,297

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/7/2013, 7:26:26 AM · Difficulty 9.9655 · 6,541,580 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

25770dea7d64deb950f5f8525ddb5ec64decca13297fc7e36a63fc744830aeea

View on Chainz ↗

Height

#248,297

Difficulty

9.965549

Transactions

Size

2.97 KB

Version

Bits

09f72e38

Nonce

4,957

Timestamp

11/7/2013, 7:26:26 AM

Confirmations

6,541,580

Merkle Root

4121acfce4c290c089b88a97e14aefa0cc64f00372082d4c293a88622bca0426

Transactions (3)

Coinbase78277dd9144a5d…ac4175e67ae803

1 in → 2 out10.0900 XPM136 B

AZDUEbdS…RYKMRZET Abiw8n3q…ZnZfgvQW

a0cd77cba47a16…415015bb14bb28

3 in → 2 out709.0100 XPM519 B

AdGYnqoY…pjMuwV34 AcDARe1P…gfSwcYEn

0b2cd37fc918c5…2c95df0f9e8404

15 in → 2 out1.5335 XPM2.25 KB

AHveP9h1…T3Qbso4W AbuQt7Hd…jcQh35eJ

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.

3.008 × 10⁹⁴(95-digit number)

30081457471509700831…86113640867780197281

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

3.008 × 10⁹⁴(95-digit number)

30081457471509700831…86113640867780197281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.016 × 10⁹⁴(95-digit number)

60162914943019401662…72227281735560394561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.203 × 10⁹⁵(96-digit number)

12032582988603880332…44454563471120789121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.406 × 10⁹⁵(96-digit number)

24065165977207760664…88909126942241578241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.813 × 10⁹⁵(96-digit number)

48130331954415521329…77818253884483156481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.626 × 10⁹⁵(96-digit number)

96260663908831042659…55636507768966312961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.925 × 10⁹⁶(97-digit number)

19252132781766208531…11273015537932625921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.850 × 10⁹⁶(97-digit number)

38504265563532417063…22546031075865251841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.700 × 10⁹⁶(97-digit number)

77008531127064834127…45092062151730503681

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.

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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