Block #51,645

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 6:45:13 AM · Difficulty 8.9014 · 6,741,095 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

728826603b2e2014aece1e072fd83df827203eccfbe8c711316b8812275ff04b

View on Chainz ↗

Height

#51,645

Difficulty

8.901401

Transactions

Size

205 B

Version

Bits

08e6c233

Nonce

1,412

Timestamp

7/16/2013, 6:45:13 AM

Confirmations

6,741,095

Merkle Root

604747b53a7e93428ec4e81f515a875befd5a07c3738c19e1bb6dd7e530fdeeb

Transactions (1)

Coinbase604747b53a7e93…b6dd7e530fdeeb

1 in → 1 out12.6000 XPM110 B

AGY4TBx7…YfD8h7Va

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.

1.682 × 10¹⁰⁶(107-digit number)

16820999099668874502…04618546993153361551

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

1.682 × 10¹⁰⁶(107-digit number)

16820999099668874502…04618546993153361551

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.364 × 10¹⁰⁶(107-digit number)

33641998199337749005…09237093986306723101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.728 × 10¹⁰⁶(107-digit number)

67283996398675498011…18474187972613446201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.345 × 10¹⁰⁷(108-digit number)

13456799279735099602…36948375945226892401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.691 × 10¹⁰⁷(108-digit number)

26913598559470199204…73896751890453784801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.382 × 10¹⁰⁷(108-digit number)

53827197118940398409…47793503780907569601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.076 × 10¹⁰⁸(109-digit number)

10765439423788079681…95587007561815139201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.153 × 10¹⁰⁸(109-digit number)

21530878847576159363…91174015123630278401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.306 × 10¹⁰⁸(109-digit number)

43061757695152318727…82348030247260556801

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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