Block #2,640,015

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/30/2018, 8:43:20 PM · Difficulty 11.5630 · 4,192,902 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1ead9aa91ce9faa93291b363ca9fab02779747d309411bf9a79a0646ee7b84cb

Height

#2,640,015

Difficulty

11.563043

Transactions

13

Size

4.29 KB

Version

2

Bits

0b902394

Nonce

199,260,309

Timestamp

4/30/2018, 8:43:20 PM

Confirmations

4,192,902

Merkle Root

c04af533aacde564078f18ad923cea0ea9932f2760f61ef57b5d2bfa2e6aaaef
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.

1.789 × 10⁹⁶(97-digit number)
17890280021579840411…36301869094413211521
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
1.789 × 10⁹⁶(97-digit number)
17890280021579840411…36301869094413211521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.578 × 10⁹⁶(97-digit number)
35780560043159680822…72603738188826423041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.156 × 10⁹⁶(97-digit number)
71561120086319361645…45207476377652846081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.431 × 10⁹⁷(98-digit number)
14312224017263872329…90414952755305692161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.862 × 10⁹⁷(98-digit number)
28624448034527744658…80829905510611384321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.724 × 10⁹⁷(98-digit number)
57248896069055489316…61659811021222768641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.144 × 10⁹⁸(99-digit number)
11449779213811097863…23319622042445537281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.289 × 10⁹⁸(99-digit number)
22899558427622195726…46639244084891074561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.579 × 10⁹⁸(99-digit number)
45799116855244391452…93278488169782149121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.159 × 10⁹⁸(99-digit number)
91598233710488782905…86556976339564298241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.831 × 10⁹⁹(100-digit number)
18319646742097756581…73113952679128596481
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:57,907,509 XPM·at block #6,832,916 · updates every 60s
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