Block #298,438

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/7/2013, 8:12:40 AM · Difficulty 9.9919 · 6,543,815 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

de9d447a9858b81b7e5ce402c50aef98929109a6782c4c3aeb8153a9f263b66f

View on Chainz ↗

Height

#298,438

Difficulty

9.991940

Transactions

Size

207 B

Version

Bits

09fdefc3

Nonce

13,942

Timestamp

12/7/2013, 8:12:40 AM

Confirmations

6,543,815

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

25152f8bfabe6f0c2b0f5e3328c0cc640119eedc88bf2224377520489c8dd55e

Transactions (1)

Coinbase25152f8bfabe6f…7520489c8dd55e

1 in → 1 out10.0000 XPM116 B

AbwWkWZt…kawDhufa

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.

6.681 × 10⁹⁷(98-digit number)

66811873873775428126…52661011415336222719

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

6.681 × 10⁹⁷(98-digit number)

66811873873775428126…52661011415336222719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.336 × 10⁹⁸(99-digit number)

13362374774755085625…05322022830672445439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.672 × 10⁹⁸(99-digit number)

26724749549510171250…10644045661344890879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.344 × 10⁹⁸(99-digit number)

53449499099020342501…21288091322689781759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.068 × 10⁹⁹(100-digit number)

10689899819804068500…42576182645379563519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.137 × 10⁹⁹(100-digit number)

21379799639608137000…85152365290759127039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.275 × 10⁹⁹(100-digit number)

42759599279216274000…70304730581518254079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.551 × 10⁹⁹(100-digit number)

85519198558432548001…40609461163036508159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.710 × 10¹⁰⁰(101-digit number)

17103839711686509600…81218922326073016319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.420 × 10¹⁰⁰(101-digit number)

34207679423373019200…62437844652146032639

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 #298,438

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