Block #192,709

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/4/2013, 1:35:26 AM · Difficulty 9.8746 · 6,598,398 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3013b9a78e6f7cfaa600713d207ea4b7bf0a5180dd826a503a78e66c18d26171

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Height

#192,709

Difficulty

9.874643

Transactions

Size

4.54 KB

Version

Bits

09dfe896

Nonce

266,327

Timestamp

10/4/2013, 1:35:26 AM

Confirmations

6,598,398

Merkle Root

44faa8375111d984d553c460d3c36264eb8a99f8b71baa796ec0331b543cde66

Transactions (2)

Coinbasea796cceede88ed…d1c196fe68beb8

1 in → 1 out10.2900 XPM109 B

AQVe2UA1…VMZmsiXq

886c002ae30072…87ddd5e233723c

38 in → 2 out380.3504 XPM4.34 KB

AKgiTbag…MJA8ujWZ AWKpUf5f…S2RLN5dS

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.

3.447 × 10⁹³(94-digit number)

34474856827350654295…82101966805592422531

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

3.447 × 10⁹³(94-digit number)

34474856827350654295…82101966805592422531

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.894 × 10⁹³(94-digit number)

68949713654701308591…64203933611184845061

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.378 × 10⁹⁴(95-digit number)

13789942730940261718…28407867222369690121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.757 × 10⁹⁴(95-digit number)

27579885461880523436…56815734444739380241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.515 × 10⁹⁴(95-digit number)

55159770923761046873…13631468889478760481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.103 × 10⁹⁵(96-digit number)

11031954184752209374…27262937778957520961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.206 × 10⁹⁵(96-digit number)

22063908369504418749…54525875557915041921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.412 × 10⁹⁵(96-digit number)

44127816739008837498…09051751115830083841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.825 × 10⁹⁵(96-digit number)

88255633478017674997…18103502231660167681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.765 × 10⁹⁶(97-digit number)

17651126695603534999…36207004463320335361

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