Block #2,655,228

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/10/2018, 12:27:03 AM · Difficulty 11.7084 · 4,178,045 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
342fa9d887216e646ef70b5da3ea16142ca895eb140cf185fb0d56e36d8e0ce9

Height

#2,655,228

Difficulty

11.708379

Transactions

2

Size

576 B

Version

2

Bits

0bb5584d

Nonce

340,856,086

Timestamp

5/10/2018, 12:27:03 AM

Confirmations

4,178,045

Merkle Root

9c9419991977947e3bd8e782545dc3b6ea05dfcdd3e7aab5f73f89992b6daf8d
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.

2.434 × 10⁹⁶(97-digit number)
24348433552693555640…25833133788080606721
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
2.434 × 10⁹⁶(97-digit number)
24348433552693555640…25833133788080606721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.869 × 10⁹⁶(97-digit number)
48696867105387111280…51666267576161213441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.739 × 10⁹⁶(97-digit number)
97393734210774222560…03332535152322426881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.947 × 10⁹⁷(98-digit number)
19478746842154844512…06665070304644853761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.895 × 10⁹⁷(98-digit number)
38957493684309689024…13330140609289707521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.791 × 10⁹⁷(98-digit number)
77914987368619378048…26660281218579415041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.558 × 10⁹⁸(99-digit number)
15582997473723875609…53320562437158830081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.116 × 10⁹⁸(99-digit number)
31165994947447751219…06641124874317660161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.233 × 10⁹⁸(99-digit number)
62331989894895502438…13282249748635320321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.246 × 10⁹⁹(100-digit number)
12466397978979100487…26564499497270640641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.493 × 10⁹⁹(100-digit number)
24932795957958200975…53128998994541281281
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:57,910,378 XPM·at block #6,833,272 · updates every 60s
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