Block #388,033

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/3/2014, 12:57:35 PM · Difficulty 10.4163 · 6,404,199 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7478167c385c5e2e820701f1e0b090e6461fa1c0f4aa05a4aef243a72e70d14a

View on Chainz ↗

Height

#388,033

Difficulty

10.416347

Transactions

Size

192 B

Version

Bits

0a6a95b5

Nonce

269,069

Timestamp

2/3/2014, 12:57:35 PM

Confirmations

6,404,199

Merkle Root

e10104d6f0a8c4755e69e80e39a2c3ea4a01e76d1336b6b995997058bce3b4dd

Transactions (1)

Coinbasee10104d6f0a8c4…997058bce3b4dd

1 in → 1 out9.2000 XPM100 B

AaXb6Ldz…XefG91jF

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.

1.645 × 10⁹⁹(100-digit number)

16451568186972478684…14985209944285126881

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

1.645 × 10⁹⁹(100-digit number)

16451568186972478684…14985209944285126881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.290 × 10⁹⁹(100-digit number)

32903136373944957369…29970419888570253761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.580 × 10⁹⁹(100-digit number)

65806272747889914738…59940839777140507521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.316 × 10¹⁰⁰(101-digit number)

13161254549577982947…19881679554281015041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.632 × 10¹⁰⁰(101-digit number)

26322509099155965895…39763359108562030081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.264 × 10¹⁰⁰(101-digit number)

52645018198311931791…79526718217124060161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.052 × 10¹⁰¹(102-digit number)

10529003639662386358…59053436434248120321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.105 × 10¹⁰¹(102-digit number)

21058007279324772716…18106872868496240641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.211 × 10¹⁰¹(102-digit number)

42116014558649545432…36213745736992481281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.423 × 10¹⁰¹(102-digit number)

84232029117299090865…72427491473984962561

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