Block #419,623

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/25/2014, 7:12:13 PM · Difficulty 10.3742 · 6,374,621 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

582d98f78b8e677563a121bfdfb2165e0fd69cb9e575225ebf25217eb8084b7a

View on Chainz ↗

Height

#419,623

Difficulty

10.374243

Transactions

Size

1.43 KB

Version

Bits

0a5fce6b

Nonce

24,761

Timestamp

2/25/2014, 7:12:13 PM

Confirmations

6,374,621

Merkle Root

3d776600810fc47902de28d6ea2f8df5d39e2d3ee0b3883ac81ba883d24370da

Transactions (2)

Coinbasee83f8c29a8d649…24c0849fd1b1e4

1 in → 1 out9.3000 XPM110 B

AeKNrjNj…1NEq95Ta

fb8f580cfaffb6…e04bb61d45c4d7

8 in → 2 out1.3829 XPM1.24 KB

AaN14Vtk…SGxMjUoW APDFiiZT…oqxnymU8

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.

1.612 × 10¹⁰¹(102-digit number)

16120023538956725842…08276186746036580061

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

1.612 × 10¹⁰¹(102-digit number)

16120023538956725842…08276186746036580061

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.224 × 10¹⁰¹(102-digit number)

32240047077913451685…16552373492073160121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.448 × 10¹⁰¹(102-digit number)

64480094155826903370…33104746984146320241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.289 × 10¹⁰²(103-digit number)

12896018831165380674…66209493968292640481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.579 × 10¹⁰²(103-digit number)

25792037662330761348…32418987936585280961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.158 × 10¹⁰²(103-digit number)

51584075324661522696…64837975873170561921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.031 × 10¹⁰³(104-digit number)

10316815064932304539…29675951746341123841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.063 × 10¹⁰³(104-digit number)

20633630129864609078…59351903492682247681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.126 × 10¹⁰³(104-digit number)

41267260259729218157…18703806985364495361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.253 × 10¹⁰³(104-digit number)

82534520519458436314…37407613970728990721

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer