Block #239,350

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/2/2013, 1:21:14 AM · Difficulty 9.9542 · 6,564,854 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b9f829a3451cd7346e4d581758b0f3bfd0c7e31a1f29aa16da65107406618268

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Height

#239,350

Difficulty

9.954225

Transactions

Size

1.78 KB

Version

Bits

09f44816

Nonce

5,160

Timestamp

11/2/2013, 1:21:14 AM

Confirmations

6,564,854

Mined by

⛏️ RtS0ANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

0dc62ec4d5d73d3c2118ce792f4fc383b45c250fd821190389878197a84e843b

Transactions (1)

Coinbase0dc62ec4d5d73d…878197a84e843b

1 in → 49 out10.0600 XPM1.69 KB

ANo4YY1x…vnsPRDSU AbeUZSvK…ijGzuyjz ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

3.547 × 10⁹⁸(99-digit number)

35474332607924992567…66406087430313522441

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

3.547 × 10⁹⁸(99-digit number)

35474332607924992567…66406087430313522441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.094 × 10⁹⁸(99-digit number)

70948665215849985135…32812174860627044881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.418 × 10⁹⁹(100-digit number)

14189733043169997027…65624349721254089761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.837 × 10⁹⁹(100-digit number)

28379466086339994054…31248699442508179521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.675 × 10⁹⁹(100-digit number)

56758932172679988108…62497398885016359041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.135 × 10¹⁰⁰(101-digit number)

11351786434535997621…24994797770032718081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.270 × 10¹⁰⁰(101-digit number)

22703572869071995243…49989595540065436161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.540 × 10¹⁰⁰(101-digit number)

45407145738143990486…99979191080130872321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.081 × 10¹⁰⁰(101-digit number)

90814291476287980973…99958382160261744641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.816 × 10¹⁰¹(102-digit number)

18162858295257596194…99916764320523489281

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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