Block #81,235

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/24/2013, 3:16:47 PM · Difficulty 9.2668 · 6,711,228 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4f705358be250dcfeca1d16af1380fec7f9778f84dea05c94d4b468f3cbb9aa3

View on Chainz ↗

Height

#81,235

Difficulty

9.266833

Transactions

Size

203 B

Version

Bits

09444f2f

Nonce

35,948

Timestamp

7/24/2013, 3:16:47 PM

Confirmations

6,711,228

Merkle Root

fc948690e90ac33dafaf916290e10677fa1cbadd39ed69fb5e331bab01bbd099

Transactions (1)

Coinbasefc948690e90ac3…331bab01bbd099

1 in → 1 out11.6300 XPM109 B

AbmC177F…pomdGgdX

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.

3.029 × 10¹⁰⁴(105-digit number)

30291916247526305979…79356053850927312819

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

3.029 × 10¹⁰⁴(105-digit number)

30291916247526305979…79356053850927312819

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.058 × 10¹⁰⁴(105-digit number)

60583832495052611959…58712107701854625639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.211 × 10¹⁰⁵(106-digit number)

12116766499010522391…17424215403709251279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.423 × 10¹⁰⁵(106-digit number)

24233532998021044783…34848430807418502559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.846 × 10¹⁰⁵(106-digit number)

48467065996042089567…69696861614837005119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.693 × 10¹⁰⁵(106-digit number)

96934131992084179135…39393723229674010239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.938 × 10¹⁰⁶(107-digit number)

19386826398416835827…78787446459348020479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.877 × 10¹⁰⁶(107-digit number)

38773652796833671654…57574892918696040959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.754 × 10¹⁰⁶(107-digit number)

77547305593667343308…15149785837392081919

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