Block #433,202

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2014, 10:36:44 AM · Difficulty 10.3428 · 6,361,685 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b94fdd780656802aa5fdafd70a837f6de63420f0eebd8a34102f16fefcb338aa

View on Chainz ↗

Height

#433,202

Difficulty

10.342793

Transactions

Size

1.48 KB

Version

Bits

0a57c150

Nonce

88,180

Timestamp

3/7/2014, 10:36:44 AM

Confirmations

6,361,685

Mined by

⛏️ 2aS.AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

98afc8927547a4abd46593846c94bcbba6d2505efbf7c9025c9a8d62669959f9

Transactions (2)

Coinbasee9e19611e1ecbb…51183cc736dbca

1 in → 24 out9.3300 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

7d2668b53fd969…56e8e6b9f38c63

2 in → 8 out9.3605 XPM545 B

AHpZVsQR…c5YYRgif AJ7bwxHw…vy276KPV AM67rT5F…RQ1YgZa4 APPZLZRh…k8wT1gVi AWpN9SZ7…cfg39PDg

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.

1.369 × 10⁹³(94-digit number)

13696078286527394778…93425799174233602501

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

1.369 × 10⁹³(94-digit number)

13696078286527394778…93425799174233602501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.739 × 10⁹³(94-digit number)

27392156573054789556…86851598348467205001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.478 × 10⁹³(94-digit number)

54784313146109579112…73703196696934410001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.095 × 10⁹⁴(95-digit number)

10956862629221915822…47406393393868820001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.191 × 10⁹⁴(95-digit number)

21913725258443831645…94812786787737640001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.382 × 10⁹⁴(95-digit number)

43827450516887663290…89625573575475280001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.765 × 10⁹⁴(95-digit number)

87654901033775326580…79251147150950560001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.753 × 10⁹⁵(96-digit number)

17530980206755065316…58502294301901120001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.506 × 10⁹⁵(96-digit number)

35061960413510130632…17004588603802240001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.012 × 10⁹⁵(96-digit number)

70123920827020261264…34009177207604480001

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