Block #519,095

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/1/2014, 12:51:33 AM · Difficulty 10.8545 · 6,284,649 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
022a536d968aef000ad11ca50ef58b9450f23d6c59293f338bc06aa71b65ae56

Height

#519,095

Difficulty

10.854527

Transactions

4

Size

870 B

Version

2

Bits

0adac240

Nonce

132,119

Timestamp

5/1/2014, 12:51:33 AM

Confirmations

6,284,649

Merkle Root

919a335adcab30419488afc483e60bfa28c5e4c21362f5847ee57474796ccbdb
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.

9.782 × 10⁹⁵(96-digit number)
97826783807549905380…59265588793770494081
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
9.782 × 10⁹⁵(96-digit number)
97826783807549905380…59265588793770494081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.956 × 10⁹⁶(97-digit number)
19565356761509981076…18531177587540988161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.913 × 10⁹⁶(97-digit number)
39130713523019962152…37062355175081976321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.826 × 10⁹⁶(97-digit number)
78261427046039924304…74124710350163952641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.565 × 10⁹⁷(98-digit number)
15652285409207984860…48249420700327905281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.130 × 10⁹⁷(98-digit number)
31304570818415969721…96498841400655810561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.260 × 10⁹⁷(98-digit number)
62609141636831939443…92997682801311621121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.252 × 10⁹⁸(99-digit number)
12521828327366387888…85995365602623242241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.504 × 10⁹⁸(99-digit number)
25043656654732775777…71990731205246484481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.008 × 10⁹⁸(99-digit number)
50087313309465551555…43981462410492968961
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:57,673,990 XPM·at block #6,803,743 · updates every 60s
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