Block #301,951

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/9/2013, 1:04:18 PM · Difficulty 9.9926 · 6,497,404 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bf99c5e89ee677ea1e84ea14c25e9b89965bcbf66c8f913475b776ab1688ddbb

View on Chainz ↗

Height

#301,951

Difficulty

9.992574

Transactions

Size

1.18 KB

Version

Bits

09fe1951

Nonce

310,504

Timestamp

12/9/2013, 1:04:18 PM

Confirmations

6,497,404

Mined by

⛏️ aRALAFH3kkjuPb935Ba7zNtVZAaHVBdunEdz

Merkle Root

6d7723b7bced30da44d75bbaf983d4f6a8271d1c07842d52744028c2fe732087

Transactions (1)

Coinbase6d7723b7bced30…4028c2fe732087

1 in → 31 out9.9800 XPM1.09 KB

ALAFH3kk…VBdunEdz AYcLTeXR…bscgPops AWQyM49v…zN9UeNMm AP35e64F…amMs1Qnk ATMdAEtZ…5XS8JqJg

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.

1.523 × 10⁹⁸(99-digit number)

15237081147993496073…14865460048815680879

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

1.523 × 10⁹⁸(99-digit number)

15237081147993496073…14865460048815680879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.047 × 10⁹⁸(99-digit number)

30474162295986992146…29730920097631361759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.094 × 10⁹⁸(99-digit number)

60948324591973984293…59461840195262723519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.218 × 10⁹⁹(100-digit number)

12189664918394796858…18923680390525447039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.437 × 10⁹⁹(100-digit number)

24379329836789593717…37847360781050894079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.875 × 10⁹⁹(100-digit number)

48758659673579187435…75694721562101788159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.751 × 10⁹⁹(100-digit number)

97517319347158374870…51389443124203576319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.950 × 10¹⁰⁰(101-digit number)

19503463869431674974…02778886248407152639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.900 × 10¹⁰⁰(101-digit number)

39006927738863349948…05557772496814305279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.801 × 10¹⁰⁰(101-digit number)

78013855477726699896…11115544993628610559

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