Block #294,603

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/4/2013, 11:15:52 PM · Difficulty 9.9911 · 6,501,870 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f36828524fb384be1b14262cb834a58c202b6d90222ec3937f2ccd9fe8b62e2e

View on Chainz ↗

Height

#294,603

Difficulty

9.991102

Transactions

Size

1.01 KB

Version

Bits

09fdb8da

Nonce

6,548

Timestamp

12/4/2013, 11:15:52 PM

Confirmations

6,501,870

Mined by

⛏️ ~aRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

511fdb577f99779f6713fbc1b992f2519db664eb7f15b9a1870872f271acbcfb

Transactions (1)

Coinbase511fdb577f9977…0872f271acbcfb

1 in → 26 out10.0000 XPM947 B

AYcLTeXR…bscgPops AHuJ9wYh…BGmgHrKZ Af4zsoYg…ZZKhD1yH AdimvR9u…9e7MP6ui Ae7UyoY4…DtgAv9cY

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.

2.033 × 10⁹⁹(100-digit number)

20332281910491890835…63851332185930738399

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

2.033 × 10⁹⁹(100-digit number)

20332281910491890835…63851332185930738399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.066 × 10⁹⁹(100-digit number)

40664563820983781671…27702664371861476799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.132 × 10⁹⁹(100-digit number)

81329127641967563342…55405328743722953599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.626 × 10¹⁰⁰(101-digit number)

16265825528393512668…10810657487445907199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.253 × 10¹⁰⁰(101-digit number)

32531651056787025337…21621314974891814399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.506 × 10¹⁰⁰(101-digit number)

65063302113574050674…43242629949783628799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.301 × 10¹⁰¹(102-digit number)

13012660422714810134…86485259899567257599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.602 × 10¹⁰¹(102-digit number)

26025320845429620269…72970519799134515199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.205 × 10¹⁰¹(102-digit number)

52050641690859240539…45941039598269030399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.041 × 10¹⁰²(103-digit number)

10410128338171848107…91882079196538060799

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