Block #318,533

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/18/2013, 10:27:41 AM · Difficulty 10.1601 · 6,481,812 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

03dda7e933faf946334f55a15a21de04d512223dd84510e7778924e648bd008b

View on Chainz ↗

Height

#318,533

Difficulty

10.160150

Transactions

Size

1.01 KB

Version

Bits

0a28ff93

Nonce

15,008

Timestamp

12/18/2013, 10:27:41 AM

Confirmations

6,481,812

Mined by

⛏️ EaRxqAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

02594cd5bfef54c6bd2fd52d150b89054b4ab19975e3b61a9326776aa44e4b5b

Transactions (1)

Coinbase02594cd5bfef54…26776aa44e4b5b

1 in → 26 out9.6700 XPM947 B

Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG Ad9pSzHt…cpJ3y2zz AJzWx2VD…j4ZSMit5 AKzkYQaQ…zR4FspJZ

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.

1.968 × 10⁹⁸(99-digit number)

19689830640937408679…57230915793849184599

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

1.968 × 10⁹⁸(99-digit number)

19689830640937408679…57230915793849184599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.937 × 10⁹⁸(99-digit number)

39379661281874817358…14461831587698369199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.875 × 10⁹⁸(99-digit number)

78759322563749634716…28923663175396738399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.575 × 10⁹⁹(100-digit number)

15751864512749926943…57847326350793476799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.150 × 10⁹⁹(100-digit number)

31503729025499853886…15694652701586953599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.300 × 10⁹⁹(100-digit number)

63007458050999707772…31389305403173907199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.260 × 10¹⁰⁰(101-digit number)

12601491610199941554…62778610806347814399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.520 × 10¹⁰⁰(101-digit number)

25202983220399883109…25557221612695628799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.040 × 10¹⁰⁰(101-digit number)

50405966440799766218…51114443225391257599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.008 × 10¹⁰¹(102-digit number)

10081193288159953243…02228886450782515199

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