Block #2,237,320

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/5/2017, 12:40:10 AM · Difficulty 10.9460 · 4,605,747 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2437cf8b41c195140f0e80e84e090f1175ff6feadb895410a7858a507b3689b8

Height

#2,237,320

Difficulty

10.946009

Transactions

2

Size

1015 B

Version

2

Bits

0af22da0

Nonce

926,080,173

Timestamp

8/5/2017, 12:40:10 AM

Confirmations

4,605,747

Merkle Root

839f438b870e2dfea74cf690b87c5f6b447a9cf1c75b7ca97f3e27af1f4d35c0
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.

8.233 × 10⁹⁵(96-digit number)
82338874181913807439…45077889880881452801
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
8.233 × 10⁹⁵(96-digit number)
82338874181913807439…45077889880881452801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.646 × 10⁹⁶(97-digit number)
16467774836382761487…90155779761762905601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.293 × 10⁹⁶(97-digit number)
32935549672765522975…80311559523525811201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.587 × 10⁹⁶(97-digit number)
65871099345531045951…60623119047051622401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.317 × 10⁹⁷(98-digit number)
13174219869106209190…21246238094103244801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.634 × 10⁹⁷(98-digit number)
26348439738212418380…42492476188206489601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.269 × 10⁹⁷(98-digit number)
52696879476424836761…84984952376412979201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.053 × 10⁹⁸(99-digit number)
10539375895284967352…69969904752825958401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.107 × 10⁹⁸(99-digit number)
21078751790569934704…39939809505651916801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.215 × 10⁹⁸(99-digit number)
42157503581139869409…79879619011303833601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
8.431 × 10⁹⁸(99-digit number)
84315007162279738818…59759238022607667201
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:57,988,894 XPM·at block #6,843,066 · updates every 60s
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