Block #519,483

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/1/2014, 6:28:43 AM · Difficulty 10.8561 · 6,283,174 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c854bf3685e57396c9d341b43d5b93c30102ec5096c6f46635dab6db97fa007d

Height

#519,483

Difficulty

10.856078

Transactions

5

Size

1.23 KB

Version

2

Bits

0adb27f3

Nonce

459,844,604

Timestamp

5/1/2014, 6:28:43 AM

Confirmations

6,283,174

Merkle Root

339c32a298407d6b6d232a025c2e963a562e0d38c84267e1c150a44c34c8cb72
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.

3.391 × 10⁹⁷(98-digit number)
33911839818097334608…27460664281762299641
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
3.391 × 10⁹⁷(98-digit number)
33911839818097334608…27460664281762299641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.782 × 10⁹⁷(98-digit number)
67823679636194669216…54921328563524599281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.356 × 10⁹⁸(99-digit number)
13564735927238933843…09842657127049198561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.712 × 10⁹⁸(99-digit number)
27129471854477867686…19685314254098397121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.425 × 10⁹⁸(99-digit number)
54258943708955735373…39370628508196794241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.085 × 10⁹⁹(100-digit number)
10851788741791147074…78741257016393588481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.170 × 10⁹⁹(100-digit number)
21703577483582294149…57482514032787176961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.340 × 10⁹⁹(100-digit number)
43407154967164588298…14965028065574353921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.681 × 10⁹⁹(100-digit number)
86814309934329176597…29930056131148707841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.736 × 10¹⁰⁰(101-digit number)
17362861986865835319…59860112262297415681
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:57,665,273 XPM·at block #6,802,656 · updates every 60s
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