Block #301,793

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/9/2013, 10:47:02 AM · Difficulty 9.9925 · 6,515,088 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6b14e81ccf8da7730a39d8c18d8a189590d7d7213fad5c61f9c24bf1e41117e2

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Height

#301,793

Difficulty

9.992541

Transactions

Size

1.11 KB

Version

Bits

09fe1726

Nonce

408,737

Timestamp

12/9/2013, 10:47:02 AM

Confirmations

6,515,088

Mined by

⛏️ aRrAc6mGvmQ9ya8dQxqWNQYGz81U4XqWmPHjR

Merkle Root

487b275d9426b47d9f92e2dad86e0e111013d12bf52a5704f4f9b1f6d155baad

Transactions (1)

Coinbase487b275d9426b4…f9b1f6d155baad

1 in → 29 out9.9800 XPM1.02 KB

Ac6mGvmQ…XqWmPHjR ASD5y7K3…PadKp2tW AHuJ9wYh…BGmgHrKZ AcP9aGkN…9c7TeeiQ AN8nUzff…YcDfRDQ2

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.

5.559 × 10⁹³(94-digit number)

55595342126451474822…18609220746265227199

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

5.559 × 10⁹³(94-digit number)

55595342126451474822…18609220746265227199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.111 × 10⁹⁴(95-digit number)

11119068425290294964…37218441492530454399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.223 × 10⁹⁴(95-digit number)

22238136850580589928…74436882985060908799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.447 × 10⁹⁴(95-digit number)

44476273701161179857…48873765970121817599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.895 × 10⁹⁴(95-digit number)

88952547402322359715…97747531940243635199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.779 × 10⁹⁵(96-digit number)

17790509480464471943…95495063880487270399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.558 × 10⁹⁵(96-digit number)

35581018960928943886…90990127760974540799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.116 × 10⁹⁵(96-digit number)

71162037921857887772…81980255521949081599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.423 × 10⁹⁶(97-digit number)

14232407584371577554…63960511043898163199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.846 × 10⁹⁶(97-digit number)

28464815168743155108…27921022087796326399

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

Block #301,793

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