Block #1,774,822

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/22/2016, 4:49:54 PM · Difficulty 10.7566 · 5,028,806 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
35159c4f3eb2044252d4e4e672393fbcf1db538c13d5db6a1de93ba75be8345b

Height

#1,774,822

Difficulty

10.756646

Transactions

3

Size

1.25 KB

Version

2

Bits

0ac1b391

Nonce

396,523,690

Timestamp

9/22/2016, 4:49:54 PM

Confirmations

5,028,806

Merkle Root

25c108e9344ca456fd5b344883013839b1e767ed394b2af7f29a15525479b705
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.

3.396 × 10⁹³(94-digit number)
33968019451285534473…16378728500029602561
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
3.396 × 10⁹³(94-digit number)
33968019451285534473…16378728500029602561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.793 × 10⁹³(94-digit number)
67936038902571068947…32757457000059205121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.358 × 10⁹⁴(95-digit number)
13587207780514213789…65514914000118410241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.717 × 10⁹⁴(95-digit number)
27174415561028427578…31029828000236820481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.434 × 10⁹⁴(95-digit number)
54348831122056855157…62059656000473640961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.086 × 10⁹⁵(96-digit number)
10869766224411371031…24119312000947281921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.173 × 10⁹⁵(96-digit number)
21739532448822742063…48238624001894563841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.347 × 10⁹⁵(96-digit number)
43479064897645484126…96477248003789127681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.695 × 10⁹⁵(96-digit number)
86958129795290968252…92954496007578255361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.739 × 10⁹⁶(97-digit number)
17391625959058193650…85908992015156510721
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:57,673,056 XPM·at block #6,803,627 · updates every 60s
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