Block #71,245

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/20/2013, 5:44:39 PM · Difficulty 8.9930 · 6,728,078 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

441d053d414a02c74a515f7327a71abb2f29ec1182b9480a3f1734b616a5a004

View on Chainz ↗

Height

#71,245

Difficulty

8.992997

Transactions

Size

202 B

Version

Bits

08fe3511

Nonce

112

Timestamp

7/20/2013, 5:44:39 PM

Confirmations

6,728,078

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

68a4bf007c331f790528721a2572d74d277134724ebdfb71d02d04a2ab9dd834

Transactions (1)

Coinbase68a4bf007c331f…2d04a2ab9dd834

1 in → 1 out12.3500 XPM110 B

AZDgU5ry…dmcwdqVC

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.

1.287 × 10¹⁰⁰(101-digit number)

12877741670142072884…35745670665460627799

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

1.287 × 10¹⁰⁰(101-digit number)

12877741670142072884…35745670665460627799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.575 × 10¹⁰⁰(101-digit number)

25755483340284145768…71491341330921255599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.151 × 10¹⁰⁰(101-digit number)

51510966680568291536…42982682661842511199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.030 × 10¹⁰¹(102-digit number)

10302193336113658307…85965365323685022399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.060 × 10¹⁰¹(102-digit number)

20604386672227316614…71930730647370044799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.120 × 10¹⁰¹(102-digit number)

41208773344454633229…43861461294740089599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.241 × 10¹⁰¹(102-digit number)

82417546688909266458…87722922589480179199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.648 × 10¹⁰²(103-digit number)

16483509337781853291…75445845178960358399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.296 × 10¹⁰²(103-digit number)

32967018675563706583…50891690357920716799

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