Block #233,330

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/29/2013, 3:47:53 PM · Difficulty 9.9425 · 6,564,804 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c5d427d7dc996962722691ea0cc357cd60dad6ae5e5f96ecdf09733e42dcdc39

View on Chainz ↗

Height

#233,330

Difficulty

9.942514

Transactions

Size

1.61 KB

Version

Bits

09f14892

Nonce

19,067

Timestamp

10/29/2013, 3:47:53 PM

Confirmations

6,564,804

Mined by

⛏️ rRoAWxMqAjDsVDnL1kBWfXmRHrWXZjNai1Anq

Merkle Root

8c709798807fa5e7808488bee78a87f49cc2b1141a8c6c6cafaa621778310695

Transactions (1)

Coinbase8c709798807fa5…aa621778310695

1 in → 44 out10.0800 XPM1.52 KB

AWxMqAjD…jNai1Anq ANuKx9Ke…wm7nrBRq AMbCuLHZ…WSoStwkc AWZb1hL4…63wEkMsn AWCfnjpk…hb1ovL8F

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.

9.000 × 10⁹⁷(98-digit number)

90007187122816195985…39796553135777520001

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

9.000 × 10⁹⁷(98-digit number)

90007187122816195985…39796553135777520001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.800 × 10⁹⁸(99-digit number)

18001437424563239197…79593106271555040001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.600 × 10⁹⁸(99-digit number)

36002874849126478394…59186212543110080001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.200 × 10⁹⁸(99-digit number)

72005749698252956788…18372425086220160001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.440 × 10⁹⁹(100-digit number)

14401149939650591357…36744850172440320001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.880 × 10⁹⁹(100-digit number)

28802299879301182715…73489700344880640001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.760 × 10⁹⁹(100-digit number)

57604599758602365430…46979400689761280001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.152 × 10¹⁰⁰(101-digit number)

11520919951720473086…93958801379522560001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.304 × 10¹⁰⁰(101-digit number)

23041839903440946172…87917602759045120001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.608 × 10¹⁰⁰(101-digit number)

46083679806881892344…75835205518090240001

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