Block #1,110,195

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/16/2015, 1:40:26 PM · Difficulty 10.8681 · 5,688,802 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3d1d40c56738bc4fc656ceb7eeaa9124fdfb8a35ec545f96b344b5ff2bf67e4d

Height

#1,110,195

Difficulty

10.868083

Transactions

2

Size

2.87 KB

Version

2

Bits

0ade3aaf

Nonce

748,124,167

Timestamp

6/16/2015, 1:40:26 PM

Confirmations

5,688,802

Merkle Root

f1b4e93c09531d4c877a914dd5d0f3b84748fa167fd08f34ced542151998cbbf
Transactions (2)
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.

3.589 × 10⁹⁴(95-digit number)
35896624636947009908…00877068761812883201
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
3.589 × 10⁹⁴(95-digit number)
35896624636947009908…00877068761812883201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.179 × 10⁹⁴(95-digit number)
71793249273894019816…01754137523625766401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.435 × 10⁹⁵(96-digit number)
14358649854778803963…03508275047251532801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.871 × 10⁹⁵(96-digit number)
28717299709557607926…07016550094503065601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.743 × 10⁹⁵(96-digit number)
57434599419115215852…14033100189006131201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.148 × 10⁹⁶(97-digit number)
11486919883823043170…28066200378012262401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.297 × 10⁹⁶(97-digit number)
22973839767646086341…56132400756024524801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.594 × 10⁹⁶(97-digit number)
45947679535292172682…12264801512049049601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.189 × 10⁹⁶(97-digit number)
91895359070584345364…24529603024098099201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.837 × 10⁹⁷(98-digit number)
18379071814116869072…49059206048196198401
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:57,636,016 XPM·at block #6,798,996 · updates every 60s
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