Block #496,066

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/16/2014, 10:05:24 PM · Difficulty 10.7486 · 6,298,287 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76ff2f9f6bd0cb4e93390d023d0273894ceb0c4721000b496205ac9f626c412f

Height

#496,066

Difficulty

10.748586

Transactions

1

Size

938 B

Version

2

Bits

0abfa350

Nonce

6,040

Timestamp

4/16/2014, 10:05:24 PM

Confirmations

6,298,287

Merkle Root

2bb5a03c3f22063a6de1241780b86cfd7277544fa106aea58761b59680eb6bf0
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.

1.368 × 10¹⁰¹(102-digit number)
13682012643980353866…27782780578764257281
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.

1
origin + 1
1.368 × 10¹⁰¹(102-digit number)
13682012643980353866…27782780578764257281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.736 × 10¹⁰¹(102-digit number)
27364025287960707732…55565561157528514561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.472 × 10¹⁰¹(102-digit number)
54728050575921415464…11131122315057029121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.094 × 10¹⁰²(103-digit number)
10945610115184283092…22262244630114058241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.189 × 10¹⁰²(103-digit number)
21891220230368566185…44524489260228116481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.378 × 10¹⁰²(103-digit number)
43782440460737132371…89048978520456232961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.756 × 10¹⁰²(103-digit number)
87564880921474264742…78097957040912465921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.751 × 10¹⁰³(104-digit number)
17512976184294852948…56195914081824931841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.502 × 10¹⁰³(104-digit number)
35025952368589705896…12391828163649863681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.005 × 10¹⁰³(104-digit number)
70051904737179411793…24783656327299727361
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, …
Circulating Supply:57,598,857 XPM·at block #6,794,352 · updates every 60s
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