Block #2,874,942

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/10/2018, 5:06:30 AM · Difficulty 11.6604 · 3,968,366 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ced8975ecf6eacb12afbfe91d7fdc9bb6d442ccbdb3c3f3bdd5809c1e4554540

Height

#2,874,942

Difficulty

11.660411

Transactions

32

Size

8.03 KB

Version

2

Bits

0ba910b9

Nonce

699,624,872

Timestamp

10/10/2018, 5:06:30 AM

Confirmations

3,968,366

Merkle Root

2a6d3f78e796ae1ba64f648dd86bcc572e6ed4c8763777bd32b07ed8264495e1
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.

9.492 × 10⁹⁶(97-digit number)
94929627674830319541…67841952192365401601
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
9.492 × 10⁹⁶(97-digit number)
94929627674830319541…67841952192365401601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.898 × 10⁹⁷(98-digit number)
18985925534966063908…35683904384730803201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.797 × 10⁹⁷(98-digit number)
37971851069932127816…71367808769461606401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.594 × 10⁹⁷(98-digit number)
75943702139864255633…42735617538923212801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.518 × 10⁹⁸(99-digit number)
15188740427972851126…85471235077846425601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.037 × 10⁹⁸(99-digit number)
30377480855945702253…70942470155692851201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.075 × 10⁹⁸(99-digit number)
60754961711891404506…41884940311385702401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.215 × 10⁹⁹(100-digit number)
12150992342378280901…83769880622771404801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.430 × 10⁹⁹(100-digit number)
24301984684756561802…67539761245542809601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.860 × 10⁹⁹(100-digit number)
48603969369513123605…35079522491085619201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.720 × 10⁹⁹(100-digit number)
97207938739026247210…70159044982171238401
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,990,830 XPM·at block #6,843,307 · updates every 60s
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