Block #98,972

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/5/2013, 11:42:45 AM · Difficulty 9.3673 · 6,727,575 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2369bf2092a56eeacca02b5e1f73ee1251a4c3eebbd4b23f2a98dc92d57f87f5

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Height

#98,972

Difficulty

9.367251

Transactions

Size

202 B

Version

Bits

095e042c

Nonce

315,457

Timestamp

8/5/2013, 11:42:45 AM

Confirmations

6,727,575

Mined by

⛏️ P2SHAMYUL1XY1HPqSCSMa5ah7SRkgVt3WZL89n

Merkle Root

266642a1899646dd2fb358b74c8a9fae2eedd58e99fe06322da207bddff80794

Transactions (1)

Coinbase266642a1899646…a207bddff80794

1 in → 1 out11.3800 XPM109 B

AMYUL1XY…t3WZL89n

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.

1.973 × 10¹⁰¹(102-digit number)

19735278352332244457…66895803204981350599

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

1.973 × 10¹⁰¹(102-digit number)

19735278352332244457…66895803204981350599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.947 × 10¹⁰¹(102-digit number)

39470556704664488914…33791606409962701199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.894 × 10¹⁰¹(102-digit number)

78941113409328977828…67583212819925402399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.578 × 10¹⁰²(103-digit number)

15788222681865795565…35166425639850804799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.157 × 10¹⁰²(103-digit number)

31576445363731591131…70332851279701609599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.315 × 10¹⁰²(103-digit number)

63152890727463182262…40665702559403219199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.263 × 10¹⁰³(104-digit number)

12630578145492636452…81331405118806438399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.526 × 10¹⁰³(104-digit number)

25261156290985272904…62662810237612876799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.052 × 10¹⁰³(104-digit number)

50522312581970545809…25325620475225753599

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 #98,972

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