Block #456,519

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/23/2014, 7:07:16 AM · Difficulty 10.4153 · 6,370,656 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6c3afa0c7c2e082cc6b67ee9468e13072d132dae1023f70568dfbde34be0b0fa

View on Chainz ↗

Height

#456,519

Difficulty

10.415297

Transactions

Size

209 B

Version

Bits

0a6a50e5

Nonce

118,968

Timestamp

3/23/2014, 7:07:16 AM

Confirmations

6,370,656

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

181f70e9fe71c3b4979dcef4a174135028c0a9ee370222b318f8acfe4cceac2f

Transactions (1)

Coinbase181f70e9fe71c3…f8acfe4cceac2f

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

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.

5.052 × 10¹⁰²(103-digit number)

50522204269955959827…28507508443837804801

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

5.052 × 10¹⁰²(103-digit number)

50522204269955959827…28507508443837804801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.010 × 10¹⁰³(104-digit number)

10104440853991191965…57015016887675609601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.020 × 10¹⁰³(104-digit number)

20208881707982383931…14030033775351219201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.041 × 10¹⁰³(104-digit number)

40417763415964767862…28060067550702438401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.083 × 10¹⁰³(104-digit number)

80835526831929535724…56120135101404876801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.616 × 10¹⁰⁴(105-digit number)

16167105366385907144…12240270202809753601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.233 × 10¹⁰⁴(105-digit number)

32334210732771814289…24480540405619507201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.466 × 10¹⁰⁴(105-digit number)

64668421465543628579…48961080811239014401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.293 × 10¹⁰⁵(106-digit number)

12933684293108725715…97922161622478028801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.586 × 10¹⁰⁵(106-digit number)

25867368586217451431…95844323244956057601

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

Block #456,519

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