Block #106,660

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/9/2013, 3:32:02 AM · Difficulty 9.6114 · 6,718,368 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

647166ad7b9a8d7ef51cb593b778dedc208df8eb2f6624349728889258f4daa7

View on Chainz ↗

Height

#106,660

Difficulty

9.611401

Transactions

Size

201 B

Version

Bits

099c84c1

Nonce

595,203

Timestamp

8/9/2013, 3:32:02 AM

Confirmations

6,718,368

Mined by

⛏️ P2SHAZ29sR79QusQVNF36wMX1odggdnKVqwKGr

Merkle Root

6ed7e680c481e0dba5fa555fcd0ea6f6897a3364671021650a9d2cb946a83146

Transactions (1)

Coinbase6ed7e680c481e0…9d2cb946a83146

1 in → 1 out10.8100 XPM109 B

AZ29sR79…nKVqwKGr

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.

5.293 × 10⁹⁹(100-digit number)

52932226538692178213…58927970245061837601

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

5.293 × 10⁹⁹(100-digit number)

52932226538692178213…58927970245061837601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.058 × 10¹⁰⁰(101-digit number)

10586445307738435642…17855940490123675201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.117 × 10¹⁰⁰(101-digit number)

21172890615476871285…35711880980247350401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.234 × 10¹⁰⁰(101-digit number)

42345781230953742570…71423761960494700801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.469 × 10¹⁰⁰(101-digit number)

84691562461907485141…42847523920989401601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.693 × 10¹⁰¹(102-digit number)

16938312492381497028…85695047841978803201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.387 × 10¹⁰¹(102-digit number)

33876624984762994056…71390095683957606401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.775 × 10¹⁰¹(102-digit number)

67753249969525988113…42780191367915212801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.355 × 10¹⁰²(103-digit number)

13550649993905197622…85560382735830425601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.710 × 10¹⁰²(103-digit number)

27101299987810395245…71120765471660851201

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

Block #106,660

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