Block #433,054

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/7/2014, 8:18:26 AM · Difficulty 10.3408 · 6,372,690 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

636e387609c25085056bd890c2b41f946fb47d5f8d829c5716e8e7ae8f9f059a

View on Chainz ↗

Height

#433,054

Difficulty

10.340840

Transactions

Size

967 B

Version

Bits

0a574149

Nonce

11,028

Timestamp

3/7/2014, 8:18:26 AM

Confirmations

6,372,690

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

0eed50affd2415026b84c02c538236f51f738c8640cc57bab03f514819069aa8

Transactions (1)

Coinbase0eed50affd2415…3f514819069aa8

1 in → 24 out9.3400 XPM877 B

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

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.

1.426 × 10⁹⁴(95-digit number)

14262562876170308701…39946952111207443441

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

1.426 × 10⁹⁴(95-digit number)

14262562876170308701…39946952111207443441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.852 × 10⁹⁴(95-digit number)

28525125752340617402…79893904222414886881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.705 × 10⁹⁴(95-digit number)

57050251504681234805…59787808444829773761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.141 × 10⁹⁵(96-digit number)

11410050300936246961…19575616889659547521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.282 × 10⁹⁵(96-digit number)

22820100601872493922…39151233779319095041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.564 × 10⁹⁵(96-digit number)

45640201203744987844…78302467558638190081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.128 × 10⁹⁵(96-digit number)

91280402407489975688…56604935117276380161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.825 × 10⁹⁶(97-digit number)

18256080481497995137…13209870234552760321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.651 × 10⁹⁶(97-digit number)

36512160962995990275…26419740469105520641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.302 × 10⁹⁶(97-digit number)

73024321925991980551…52839480938211041281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.460 × 10⁹⁷(98-digit number)

14604864385198396110…05678961876422082561

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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