Block #430,285

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/5/2014, 9:51:48 AM · Difficulty 10.3417 · 6,374,031 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

be35edd5d81ca04d222a274b2f3785065cd9ffd9043d9e19cdaf46aadd8196e9

View on Chainz ↗

Height

#430,285

Difficulty

10.341742

Transactions

Size

969 B

Version

Bits

0a577c6b

Nonce

1,790

Timestamp

3/5/2014, 9:51:48 AM

Confirmations

6,374,031

Mined by

⛏️ aSBAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c3fc3a9f6b500e301f131e596d276326b44bbb94cb73db0ef4aa76a1a6b313e7

Transactions (1)

Coinbasec3fc3a9f6b500e…aa76a1a6b313e7

1 in → 24 out9.3400 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 Aaffr4EL…bJQCxKCY

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.

3.744 × 10⁹⁵(96-digit number)

37447979900288306104…89827498397503472641

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

3.744 × 10⁹⁵(96-digit number)

37447979900288306104…89827498397503472641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.489 × 10⁹⁵(96-digit number)

74895959800576612208…79654996795006945281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.497 × 10⁹⁶(97-digit number)

14979191960115322441…59309993590013890561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.995 × 10⁹⁶(97-digit number)

29958383920230644883…18619987180027781121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.991 × 10⁹⁶(97-digit number)

59916767840461289766…37239974360055562241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.198 × 10⁹⁷(98-digit number)

11983353568092257953…74479948720111124481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.396 × 10⁹⁷(98-digit number)

23966707136184515906…48959897440222248961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.793 × 10⁹⁷(98-digit number)

47933414272369031813…97919794880444497921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.586 × 10⁹⁷(98-digit number)

95866828544738063626…95839589760888995841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.917 × 10⁹⁸(99-digit number)

19173365708947612725…91679179521777991681

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