Block #98,392

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/5/2013, 5:16:29 AM · Difficulty 9.3420 · 6,695,776 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

18abc54c60d0306633dc1cbc58f123b6653c001e9b1a375f05e4540f655bff19

View on Chainz ↗

Height

#98,392

Difficulty

9.341978

Transactions

Size

1.94 KB

Version

Bits

09578bde

Nonce

53,550

Timestamp

8/5/2013, 5:16:29 AM

Confirmations

6,695,776

Merkle Root

23a8cce4ec44d9aef9c8e15f5894e29079cbd70ce992956fdaf26b43571dce22

Transactions (3)

Coinbase780def407e4772…bff291aede7951

1 in → 1 out11.4600 XPM109 B

AMgcwvpW…xCnWAEEV

a3bee24732735d…070f70d0e2e403

5 in → 2 out46.4229 XPM817 B

AQpksQD7…uFeoUDiA AKZHGNpJ…FByhphHp

1797de910f4b52…2da605601a6afd

6 in → 2 out52.1100 XPM964 B

AJt1FPie…R9BL9EmJ AcJnSyvn…VijA5cNC

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.

1.078 × 10¹⁰⁰(101-digit number)

10789172953420334153…07250866027373508359

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

1.078 × 10¹⁰⁰(101-digit number)

10789172953420334153…07250866027373508359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.157 × 10¹⁰⁰(101-digit number)

21578345906840668306…14501732054747016719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.315 × 10¹⁰⁰(101-digit number)

43156691813681336613…29003464109494033439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.631 × 10¹⁰⁰(101-digit number)

86313383627362673226…58006928218988066879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.726 × 10¹⁰¹(102-digit number)

17262676725472534645…16013856437976133759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.452 × 10¹⁰¹(102-digit number)

34525353450945069290…32027712875952267519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.905 × 10¹⁰¹(102-digit number)

69050706901890138580…64055425751904535039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.381 × 10¹⁰²(103-digit number)

13810141380378027716…28110851503809070079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.762 × 10¹⁰²(103-digit number)

27620282760756055432…56221703007618140159

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