Block #98,973

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/5/2013, 11:43:39 AM · Difficulty 9.3673 · 6,728,110 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4fc767f8cf1d658428f3f1edbbd6197e8a7888f954b24da4fd76344c6fb53c63

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Height

#98,973

Difficulty

9.367255

Transactions

Size

204 B

Version

Bits

095e0473

Nonce

154,319

Timestamp

8/5/2013, 11:43:39 AM

Confirmations

6,728,110

Mined by

⛏️ P2SHAemxcyphd8pkHc2SYoV7iRYUjn5SUkNz3q

Merkle Root

8de2bf2c2937edff76e17725802edd91347ac89ff5113d270649996f15893a1d

Transactions (1)

Coinbase8de2bf2c2937ed…49996f15893a1d

1 in → 1 out11.3800 XPM109 B

Aemxcyph…5SUkNz3q

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.

1.400 × 10¹⁰⁷(108-digit number)

14003521374608417676…91058112347305131519

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

1.400 × 10¹⁰⁷(108-digit number)

14003521374608417676…91058112347305131519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.800 × 10¹⁰⁷(108-digit number)

28007042749216835353…82116224694610263039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.601 × 10¹⁰⁷(108-digit number)

56014085498433670706…64232449389220526079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.120 × 10¹⁰⁸(109-digit number)

11202817099686734141…28464898778441052159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.240 × 10¹⁰⁸(109-digit number)

22405634199373468282…56929797556882104319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.481 × 10¹⁰⁸(109-digit number)

44811268398746936564…13859595113764208639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.962 × 10¹⁰⁸(109-digit number)

89622536797493873129…27719190227528417279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.792 × 10¹⁰⁹(110-digit number)

17924507359498774625…55438380455056834559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.584 × 10¹⁰⁹(110-digit number)

35849014718997549251…10876760910113669119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #98,973

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