Block #150,870

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/5/2013, 8:01:28 AM · Difficulty 9.8589 · 6,638,964 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c89c8b505cf033e3a457b953f33f2ce1051eef3fd391301c0cb6efa9934559df

View on Chainz ↗

Height

#150,870

Difficulty

9.858930

Transactions

Size

198 B

Version

Bits

09dbe2ce

Nonce

31,801

Timestamp

9/5/2013, 8:01:28 AM

Confirmations

6,638,964

Merkle Root

ae0f30e18474c6010a0f5694ad8ad2c6c26c18cf280a74a862919dfdddf5304c

Transactions (1)

Coinbaseae0f30e18474c6…919dfdddf5304c

1 in → 1 out10.2700 XPM109 B

AZv7gMUK…CbiASjGW

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.

3.084 × 10⁹²(93-digit number)

30843495724986596216…60620333449286190881

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

3.084 × 10⁹²(93-digit number)

30843495724986596216…60620333449286190881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.168 × 10⁹²(93-digit number)

61686991449973192432…21240666898572381761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.233 × 10⁹³(94-digit number)

12337398289994638486…42481333797144763521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.467 × 10⁹³(94-digit number)

24674796579989276973…84962667594289527041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.934 × 10⁹³(94-digit number)

49349593159978553946…69925335188579054081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.869 × 10⁹³(94-digit number)

98699186319957107892…39850670377158108161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.973 × 10⁹⁴(95-digit number)

19739837263991421578…79701340754316216321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.947 × 10⁹⁴(95-digit number)

39479674527982843156…59402681508632432641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.895 × 10⁹⁴(95-digit number)

78959349055965686313…18805363017264865281

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.

★☆☆☆☆

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