Block #31,220

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/13/2013, 10:33:44 PM · Difficulty 7.9883 · 6,779,035 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

45feec0c2c49592e8b4f84bb1f0ab3de0f71196d423e7f75841087d55bda92d8

View on Chainz ↗

Height

#31,220

Difficulty

7.988308

Transactions

Size

204 B

Version

Bits

07fd01c7

Nonce

421

Timestamp

7/13/2013, 10:33:44 PM

Confirmations

6,779,035

Mined by

⛏️ P2SHAKSwr9eUsXtYAeGKZ6MmF96jvsdLNxuVyn

Merkle Root

68f6b2e3a5f23f9461b04bd225f1b00781f8fb3affebe0a351f4c7535a2e2831

Transactions (1)

Coinbase68f6b2e3a5f23f…f4c7535a2e2831

1 in → 1 out15.6500 XPM109 B

AKSwr9eU…dLNxuVyn

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.

2.184 × 10¹⁰⁷(108-digit number)

21846045777310714163…92483369736571825279

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

2.184 × 10¹⁰⁷(108-digit number)

21846045777310714163…92483369736571825279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.369 × 10¹⁰⁷(108-digit number)

43692091554621428326…84966739473143650559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.738 × 10¹⁰⁷(108-digit number)

87384183109242856653…69933478946287301119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.747 × 10¹⁰⁸(109-digit number)

17476836621848571330…39866957892574602239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.495 × 10¹⁰⁸(109-digit number)

34953673243697142661…79733915785149204479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.990 × 10¹⁰⁸(109-digit number)

69907346487394285323…59467831570298408959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.398 × 10¹⁰⁹(110-digit number)

13981469297478857064…18935663140596817919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.796 × 10¹⁰⁹(110-digit number)

27962938594957714129…37871326281193635839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #31,220

Cookie Preferences