Block #2,643,246

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/2/2018, 12:59:50 AM · Difficulty 11.6778 · 4,189,152 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5487e2f2f41c3e15c47c50134ef33377ba6e37e3e19814aff2ab3e3d2fdad1ff

Height

#2,643,246

Difficulty

11.677777

Transactions

3

Size

653 B

Version

2

Bits

0bad82ca

Nonce

503,175,315

Timestamp

5/2/2018, 12:59:50 AM

Confirmations

4,189,152

Merkle Root

b8c0ddb8cb09f30b70a511bf44e31bd054f6a4124cbee483797afe98db423003
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.

1.891 × 10⁹⁶(97-digit number)
18910841937685832946…57464810464732751041
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
1.891 × 10⁹⁶(97-digit number)
18910841937685832946…57464810464732751041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.782 × 10⁹⁶(97-digit number)
37821683875371665893…14929620929465502081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.564 × 10⁹⁶(97-digit number)
75643367750743331787…29859241858931004161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.512 × 10⁹⁷(98-digit number)
15128673550148666357…59718483717862008321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.025 × 10⁹⁷(98-digit number)
30257347100297332715…19436967435724016641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.051 × 10⁹⁷(98-digit number)
60514694200594665430…38873934871448033281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.210 × 10⁹⁸(99-digit number)
12102938840118933086…77747869742896066561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.420 × 10⁹⁸(99-digit number)
24205877680237866172…55495739485792133121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.841 × 10⁹⁸(99-digit number)
48411755360475732344…10991478971584266241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.682 × 10⁹⁸(99-digit number)
96823510720951464688…21982957943168532481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.936 × 10⁹⁹(100-digit number)
19364702144190292937…43965915886337064961
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:57,903,327 XPM·at block #6,832,397 · updates every 60s
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