Block #302,044

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/9/2013, 2:18:59 PM · Difficulty 9.9926 · 6,501,010 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8991d910667110879de095281ee6193349af2f1ebfd913da19f4b045a1f71a61

View on Chainz ↗

Height

#302,044

Difficulty

9.992604

Transactions

Size

1.15 KB

Version

Bits

09fe1b49

Nonce

7,158

Timestamp

12/9/2013, 2:18:59 PM

Confirmations

6,501,010

Mined by

⛏️ aR8@AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

12a89bec00b80b9dd5c67aef48e48d619fc6d301c5571772b957dcf87f38bbeb

Transactions (1)

Coinbase12a89bec00b80b…57dcf87f38bbeb

1 in → 30 out9.9800 XPM1.06 KB

AHuJ9wYh…BGmgHrKZ APeshfYV…3PKcKMKH Ad9pSzHt…cpJ3y2zz AN8nUzff…YcDfRDQ2 AQXnpn5q…EBB2btkd

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.

6.823 × 10⁹⁹(100-digit number)

68233444536890621759…57413254684308079999

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

6.823 × 10⁹⁹(100-digit number)

68233444536890621759…57413254684308079999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.364 × 10¹⁰⁰(101-digit number)

13646688907378124351…14826509368616159999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.729 × 10¹⁰⁰(101-digit number)

27293377814756248703…29653018737232319999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.458 × 10¹⁰⁰(101-digit number)

54586755629512497407…59306037474464639999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.091 × 10¹⁰¹(102-digit number)

10917351125902499481…18612074948929279999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.183 × 10¹⁰¹(102-digit number)

21834702251804998962…37224149897858559999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.366 × 10¹⁰¹(102-digit number)

43669404503609997925…74448299795717119999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.733 × 10¹⁰¹(102-digit number)

87338809007219995851…48896599591434239999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.746 × 10¹⁰²(103-digit number)

17467761801443999170…97793199182868479999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.493 × 10¹⁰²(103-digit number)

34935523602887998340…95586398365736959999

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