Block #2,649,922

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/5/2018, 3:23:30 PM · Difficulty 11.7606 · 4,189,087 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ce460bed3f9d394b588afde7fbe873e45250f55ad6848a933d2ad50a61ce2854

Height

#2,649,922

Difficulty

11.760644

Transactions

3

Size

882 B

Version

2

Bits

0bc2b990

Nonce

12,795,188

Timestamp

5/5/2018, 3:23:30 PM

Confirmations

4,189,087

Merkle Root

28b5f6d9bd88f37ce9ff21a8dfc052f83badec0fd67608c2c99a22b1caaf4f3a
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.

1.152 × 10⁹⁵(96-digit number)
11523805425993884894…48426825752546981481
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
1.152 × 10⁹⁵(96-digit number)
11523805425993884894…48426825752546981481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.304 × 10⁹⁵(96-digit number)
23047610851987769788…96853651505093962961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.609 × 10⁹⁵(96-digit number)
46095221703975539577…93707303010187925921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.219 × 10⁹⁵(96-digit number)
92190443407951079155…87414606020375851841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.843 × 10⁹⁶(97-digit number)
18438088681590215831…74829212040751703681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.687 × 10⁹⁶(97-digit number)
36876177363180431662…49658424081503407361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.375 × 10⁹⁶(97-digit number)
73752354726360863324…99316848163006814721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.475 × 10⁹⁷(98-digit number)
14750470945272172664…98633696326013629441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.950 × 10⁹⁷(98-digit number)
29500941890544345329…97267392652027258881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.900 × 10⁹⁷(98-digit number)
59001883781088690659…94534785304054517761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.180 × 10⁹⁸(99-digit number)
11800376756217738131…89069570608109035521
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:57,956,338 XPM·at block #6,839,008 · updates every 60s
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