Block #399,942

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/11/2014, 5:42:25 PM · Difficulty 10.4325 · 6,403,750 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e43707595c6d113fd72f9ec0665ee3bc88cae7bdda88534c2474ffaa7eb5b463

View on Chainz ↗

Height

#399,942

Difficulty

10.432476

Transactions

Size

968 B

Version

Bits

0a6eb6c4

Nonce

202,124

Timestamp

2/11/2014, 5:42:25 PM

Confirmations

6,403,750

Mined by

⛏️ FaR`AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

fe87c6a0abd0d11eb2bf80df9ba7f2502b04d5bd35635b54adf1ac5951d007fe

Transactions (1)

Coinbasefe87c6a0abd0d1…f1ac5951d007fe

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 AUnkFe8H…fvenjA4X ATnPEc1T…ndE5zGvr

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.

9.285 × 10⁹²(93-digit number)

92857920675745653929…82699283148502859729

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

9.285 × 10⁹²(93-digit number)

92857920675745653929…82699283148502859729

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.857 × 10⁹³(94-digit number)

18571584135149130785…65398566297005719459

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.714 × 10⁹³(94-digit number)

37143168270298261571…30797132594011438919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.428 × 10⁹³(94-digit number)

74286336540596523143…61594265188022877839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.485 × 10⁹⁴(95-digit number)

14857267308119304628…23188530376045755679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.971 × 10⁹⁴(95-digit number)

29714534616238609257…46377060752091511359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.942 × 10⁹⁴(95-digit number)

59429069232477218514…92754121504183022719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.188 × 10⁹⁵(96-digit number)

11885813846495443702…85508243008366045439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.377 × 10⁹⁵(96-digit number)

23771627692990887405…71016486016732090879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.754 × 10⁹⁵(96-digit number)

47543255385981774811…42032972033464181759

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