Block #2,646,077

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2018, 4:47:21 AM · Difficulty 11.7443 · 4,185,039 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9838388d5882f5ab0cbccc46f7516795dbd90f50dcb3945117dd2729f4fbfe30

Height

#2,646,077

Difficulty

11.744305

Transactions

2

Size

607 B

Version

2

Bits

0bbe8ac1

Nonce

378,509,818

Timestamp

5/3/2018, 4:47:21 AM

Confirmations

4,185,039

Merkle Root

116d9d126a60700f5e7669e6023ecd6df19dc644c779ae429291a5f582f247e9
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.

5.252 × 10⁹²(93-digit number)
52528397417482016473…90570696185724701681
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
5.252 × 10⁹²(93-digit number)
52528397417482016473…90570696185724701681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.050 × 10⁹³(94-digit number)
10505679483496403294…81141392371449403361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.101 × 10⁹³(94-digit number)
21011358966992806589…62282784742898806721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.202 × 10⁹³(94-digit number)
42022717933985613179…24565569485797613441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.404 × 10⁹³(94-digit number)
84045435867971226358…49131138971595226881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.680 × 10⁹⁴(95-digit number)
16809087173594245271…98262277943190453761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.361 × 10⁹⁴(95-digit number)
33618174347188490543…96524555886380907521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.723 × 10⁹⁴(95-digit number)
67236348694376981086…93049111772761815041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.344 × 10⁹⁵(96-digit number)
13447269738875396217…86098223545523630081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.689 × 10⁹⁵(96-digit number)
26894539477750792434…72196447091047260161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.378 × 10⁹⁵(96-digit number)
53789078955501584869…44392894182094520321
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:57,893,073 XPM·at block #6,831,115 · updates every 60s
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