Block #243,173

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/4/2013, 3:44:08 AM · Difficulty 9.9611 · 6,556,156 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0359f1fe946ff636e1f2f88158eab1464f22adce5138eea9af5bf42018d74180

View on Chainz ↗

Height

#243,173

Difficulty

9.961102

Transactions

Size

1.94 KB

Version

Bits

09f60ac8

Nonce

19,716

Timestamp

11/4/2013, 3:44:08 AM

Confirmations

6,556,156

Mined by

⛏️ Rw_AUT1qxTxv3avbJ532uNhHh1mRst5B3qd8Z

Merkle Root

2fc9b3315f8111b6bec9f55b5cc083db44c1280a855f8726d81b8d316cf9f826

Transactions (1)

Coinbase2fc9b3315f8111…1b8d316cf9f826

1 in → 54 out10.0372 XPM1.85 KB

AUT1qxTx…t5B3qd8Z ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AMttQDuf…7j6tfS9x AG32MWye…bvPnrq7k

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.

1.045 × 10⁹³(94-digit number)

10451854239999396598…65812569649105098741

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

1.045 × 10⁹³(94-digit number)

10451854239999396598…65812569649105098741

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.090 × 10⁹³(94-digit number)

20903708479998793196…31625139298210197481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.180 × 10⁹³(94-digit number)

41807416959997586393…63250278596420394961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.361 × 10⁹³(94-digit number)

83614833919995172786…26500557192840789921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.672 × 10⁹⁴(95-digit number)

16722966783999034557…53001114385681579841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.344 × 10⁹⁴(95-digit number)

33445933567998069114…06002228771363159681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.689 × 10⁹⁴(95-digit number)

66891867135996138229…12004457542726319361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.337 × 10⁹⁵(96-digit number)

13378373427199227645…24008915085452638721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.675 × 10⁹⁵(96-digit number)

26756746854398455291…48017830170905277441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.351 × 10⁹⁵(96-digit number)

53513493708796910583…96035660341810554881

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