Block #360,873

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/15/2014, 5:18:12 PM · Difficulty 10.4001 · 6,444,299 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b3b5443e55725910e89962a5b7ff4e43797b6dc8cff85ca110fe495f6ad71839

View on Chainz ↗

Height

#360,873

Difficulty

10.400116

Transactions

Size

1.14 KB

Version

Bits

0a666dfa

Nonce

27,925

Timestamp

1/15/2014, 5:18:12 PM

Confirmations

6,444,299

Mined by

⛏️ P2SHAWtUQKW6dWZWXbNDYMdYSDsJbxBYdycPoC

Merkle Root

aa84f09b9e9293247f184cbbca0546ac34f5d0afc31bf46d731e6293a5c60336

Transactions (2)

Coinbase5a1c47160c74ed…c8e45ef8d75f6a

1 in → 1 out9.2400 XPM109 B

AWtUQKW6…BYdycPoC

1d83efe24adc63…b978682dc708ee

6 in → 2 out51.7976 XPM967 B

AdSUUtTv…hsQuK5wR AcGD1LHJ…ZHgx9g48

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.

4.475 × 10⁹⁷(98-digit number)

44755675441118966025…44489994421037811839

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

4.475 × 10⁹⁷(98-digit number)

44755675441118966025…44489994421037811839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.951 × 10⁹⁷(98-digit number)

89511350882237932051…88979988842075623679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.790 × 10⁹⁸(99-digit number)

17902270176447586410…77959977684151247359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.580 × 10⁹⁸(99-digit number)

35804540352895172820…55919955368302494719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.160 × 10⁹⁸(99-digit number)

71609080705790345641…11839910736604989439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.432 × 10⁹⁹(100-digit number)

14321816141158069128…23679821473209978879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.864 × 10⁹⁹(100-digit number)

28643632282316138256…47359642946419957759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.728 × 10⁹⁹(100-digit number)

57287264564632276512…94719285892839915519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.145 × 10¹⁰⁰(101-digit number)

11457452912926455302…89438571785679831039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.291 × 10¹⁰⁰(101-digit number)

22914905825852910605…78877143571359662079

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer