Block #1,440,707

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/3/2016, 9:08:26 AM · Difficulty 10.7667 · 5,363,370 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fd4eee2ebd02f695ed6d04d0de3392c0fb96a57e37dccca72018fa6505d53afa

View on Chainz ↗

Height

#1,440,707

Difficulty

10.766721

Transactions

Size

202 B

Version

Bits

0ac447d6

Nonce

342,813

Timestamp

2/3/2016, 9:08:26 AM

Confirmations

5,363,370

Mined by

⛏️ P2SHAVUSTGLfXSGYjUDuVVpW48qmaeSeYSsAGR

Merkle Root

5ba735c9dc104016d7de55ad0ee77a0010015466bbaf7e4362fe0f7ccbd8a1cf

Transactions (1)

Coinbase5ba735c9dc1040…fe0f7ccbd8a1cf

1 in → 1 out8.6100 XPM109 B

AVUSTGLf…SeYSsAGR

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.

9.282 × 10¹⁰⁰(101-digit number)

92824919863717888561…56386619746918316319

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

9.282 × 10¹⁰⁰(101-digit number)

92824919863717888561…56386619746918316319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.856 × 10¹⁰¹(102-digit number)

18564983972743577712…12773239493836632639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.712 × 10¹⁰¹(102-digit number)

37129967945487155424…25546478987673265279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.425 × 10¹⁰¹(102-digit number)

74259935890974310849…51092957975346530559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.485 × 10¹⁰²(103-digit number)

14851987178194862169…02185915950693061119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.970 × 10¹⁰²(103-digit number)

29703974356389724339…04371831901386122239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.940 × 10¹⁰²(103-digit number)

59407948712779448679…08743663802772244479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.188 × 10¹⁰³(104-digit number)

11881589742555889735…17487327605544488959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.376 × 10¹⁰³(104-digit number)

23763179485111779471…34974655211088977919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.752 × 10¹⁰³(104-digit number)

47526358970223558943…69949310422177955839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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