Block #919,466

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/2/2015, 5:01:12 AM · Difficulty 10.9203 · 5,885,555 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ad67e11da0dc55e17f50fee4c60642a8c9d1266b9e3b885f498843aa65a184a

Height

#919,466

Difficulty

10.920306

Transactions

5

Size

43.72 KB

Version

2

Bits

0aeb9930

Nonce

780,138,726

Timestamp

2/2/2015, 5:01:12 AM

Confirmations

5,885,555

Merkle Root

caf9208647f97e3665e00f6124b74bbaea42cbc45567689a3c73991fe587d921
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.

5.133 × 10⁹⁵(96-digit number)
51331150822717400029…94494351863863564001
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
5.133 × 10⁹⁵(96-digit number)
51331150822717400029…94494351863863564001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.026 × 10⁹⁶(97-digit number)
10266230164543480005…88988703727727128001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.053 × 10⁹⁶(97-digit number)
20532460329086960011…77977407455454256001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.106 × 10⁹⁶(97-digit number)
41064920658173920023…55954814910908512001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.212 × 10⁹⁶(97-digit number)
82129841316347840046…11909629821817024001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.642 × 10⁹⁷(98-digit number)
16425968263269568009…23819259643634048001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.285 × 10⁹⁷(98-digit number)
32851936526539136018…47638519287268096001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.570 × 10⁹⁷(98-digit number)
65703873053078272037…95277038574536192001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.314 × 10⁹⁸(99-digit number)
13140774610615654407…90554077149072384001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.628 × 10⁹⁸(99-digit number)
26281549221231308814…81108154298144768001
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:57,684,232 XPM·at block #6,805,020 · updates every 60s
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