Block #234,125

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/30/2013, 3:39:25 AM · Difficulty 9.9435 · 6,557,704 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a1c2bb307d3c76b6b50c9cbcd2d7201e890e49cedc6b39984c7cdb467456deeb

View on Chainz ↗

Height

#234,125

Difficulty

9.943499

Transactions

Size

1.36 KB

Version

Bits

09f1891f

Nonce

10,578

Timestamp

10/30/2013, 3:39:25 AM

Confirmations

6,557,704

Merkle Root

507688628fc5b9ad63865fdfaa691f59c690e99e2337393210ea3e6eda8f5085

Transactions (3)

Coinbase8c4e5ca25c30ee…4dc24503924bec

1 in → 1 out10.1300 XPM109 B

AHPLSWVd…ZdicvSUu

9f941f4a824d96…c651cf92a805f3

6 in → 2 out30.0815 XPM969 B

AQYBnS82…5vUnLk96 AZoTowvW…KJoS4PJA

a675e3e4020dbd…0253dc53f9e12a

1 in → 2 out8.0873 XPM227 B

AKRrUtNT…G82cPzyD AY1ZK2KH…EFd4Jne1

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.

2.552 × 10⁹⁹(100-digit number)

25529773756127762424…40833537545636807679

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

2.552 × 10⁹⁹(100-digit number)

25529773756127762424…40833537545636807679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.105 × 10⁹⁹(100-digit number)

51059547512255524848…81667075091273615359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.021 × 10¹⁰⁰(101-digit number)

10211909502451104969…63334150182547230719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.042 × 10¹⁰⁰(101-digit number)

20423819004902209939…26668300365094461439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.084 × 10¹⁰⁰(101-digit number)

40847638009804419879…53336600730188922879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.169 × 10¹⁰⁰(101-digit number)

81695276019608839758…06673201460377845759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.633 × 10¹⁰¹(102-digit number)

16339055203921767951…13346402920755691519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.267 × 10¹⁰¹(102-digit number)

32678110407843535903…26692805841511383039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.535 × 10¹⁰¹(102-digit number)

65356220815687071806…53385611683022766079

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