Block #2,377,884

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/13/2017, 4:16:46 PM · Difficulty 10.8797 · 4,465,099 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a213c2ac30671ba2fd7a93795e18dfb59727e1607749ade076231502400b4907

Height

#2,377,884

Difficulty

10.879684

Transactions

3

Size

4.10 KB

Version

2

Bits

0ae132fd

Nonce

237,957,913

Timestamp

11/13/2017, 4:16:46 PM

Confirmations

4,465,099

Merkle Root

724e543704920471ed4b69c83c95e916139714ffcfb6ae316f7798412d2f6cd6
Transactions (3)
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.

1.819 × 10⁹⁵(96-digit number)
18198608826956509236…27881617020932044801
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
1.819 × 10⁹⁵(96-digit number)
18198608826956509236…27881617020932044801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.639 × 10⁹⁵(96-digit number)
36397217653913018473…55763234041864089601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.279 × 10⁹⁵(96-digit number)
72794435307826036946…11526468083728179201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.455 × 10⁹⁶(97-digit number)
14558887061565207389…23052936167456358401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.911 × 10⁹⁶(97-digit number)
29117774123130414778…46105872334912716801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.823 × 10⁹⁶(97-digit number)
58235548246260829557…92211744669825433601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.164 × 10⁹⁷(98-digit number)
11647109649252165911…84423489339650867201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.329 × 10⁹⁷(98-digit number)
23294219298504331822…68846978679301734401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.658 × 10⁹⁷(98-digit number)
46588438597008663645…37693957358603468801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.317 × 10⁹⁷(98-digit number)
93176877194017327291…75387914717206937601
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:57,988,218 XPM·at block #6,842,982 · updates every 60s
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