Block #514

2CCLength 7★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/8/2013, 1:23:04 AM · Difficulty 7.0206 · 6,805,334 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c05bafa31892cbdfc52818737aeedf87605ef3085a2be97f4bb52461b4eaef06

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Height

#514

Difficulty

7.020634

Transactions

Size

195 B

Version

Bits

0705483f

Nonce

272

Timestamp

7/8/2013, 1:23:04 AM

Confirmations

6,805,334

Mined by

⛏️ P2SHAMqUNXEt5v5VxTm6yhWr3LdqqJYKyzL6uS

Merkle Root

018feac58bbe125ba2d45e7dadda08ffe69ed329697077f10f2166a1e5b80393

Transactions (1)

Coinbase018feac58bbe12…2166a1e5b80393

1 in → 1 out20.2600 XPM108 B

AMqUNXEt…YKyzL6uS

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.

2.895 × 10⁸⁸(89-digit number)

28950537510822539783…06821303128851496251

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

2.895 × 10⁸⁸(89-digit number)

28950537510822539783…06821303128851496251

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.790 × 10⁸⁸(89-digit number)

57901075021645079567…13642606257702992501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.158 × 10⁸⁹(90-digit number)

11580215004329015913…27285212515405985001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.316 × 10⁸⁹(90-digit number)

23160430008658031826…54570425030811970001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.632 × 10⁸⁹(90-digit number)

46320860017316063653…09140850061623940001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.264 × 10⁸⁹(90-digit number)

92641720034632127307…18281700123247880001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.852 × 10⁹⁰(91-digit number)

18528344006926425461…36563400246495760001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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