Block #1,119,191

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/20/2015, 9:14:31 AM · Difficulty 10.9344 · 5,697,355 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f5fed22c076a761cda25060385b21a83608aeb0ecf79c4e0ec1e7022a7cdfe1f

Height

#1,119,191

Difficulty

10.934362

Transactions

5

Size

38.37 KB

Version

2

Bits

0aef325c

Nonce

995,329,375

Timestamp

6/20/2015, 9:14:31 AM

Confirmations

5,697,355

Merkle Root

229a13eb92bd76ebbfba2c7306195117627efabc091733628fe1f9d92546f755
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.

3.522 × 10⁹¹(92-digit number)
35227038570376142313…72573252617089729001
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
3.522 × 10⁹¹(92-digit number)
35227038570376142313…72573252617089729001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.045 × 10⁹¹(92-digit number)
70454077140752284626…45146505234179458001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.409 × 10⁹²(93-digit number)
14090815428150456925…90293010468358916001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.818 × 10⁹²(93-digit number)
28181630856300913850…80586020936717832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.636 × 10⁹²(93-digit number)
56363261712601827701…61172041873435664001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.127 × 10⁹³(94-digit number)
11272652342520365540…22344083746871328001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.254 × 10⁹³(94-digit number)
22545304685040731080…44688167493742656001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.509 × 10⁹³(94-digit number)
45090609370081462160…89376334987485312001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.018 × 10⁹³(94-digit number)
90181218740162924321…78752669974970624001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.803 × 10⁹⁴(95-digit number)
18036243748032584864…57505339949941248001
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:57,776,497 XPM·at block #6,816,545 · updates every 60s
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