Block #2,646,276

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/3/2018, 7:03:19 AM · Difficulty 11.7475 · 4,186,885 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6462356453ded9fccd9a1e69b77559b4c6fb75bbd4e3c14664f5203214421ba7

Height

#2,646,276

Difficulty

11.747487

Transactions

2

Size

425 B

Version

2

Bits

0bbf5b4c

Nonce

673,631,956

Timestamp

5/3/2018, 7:03:19 AM

Confirmations

4,186,885

Merkle Root

a9857433290e2fec3da9220bf27af3d2fd410ef27bb79b37f78635f473a03f1b
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.

2.384 × 10⁹⁵(96-digit number)
23843631737597212685…82742955767034751001
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
2.384 × 10⁹⁵(96-digit number)
23843631737597212685…82742955767034751001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.768 × 10⁹⁵(96-digit number)
47687263475194425370…65485911534069502001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.537 × 10⁹⁵(96-digit number)
95374526950388850741…30971823068139004001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.907 × 10⁹⁶(97-digit number)
19074905390077770148…61943646136278008001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.814 × 10⁹⁶(97-digit number)
38149810780155540296…23887292272556016001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.629 × 10⁹⁶(97-digit number)
76299621560311080593…47774584545112032001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.525 × 10⁹⁷(98-digit number)
15259924312062216118…95549169090224064001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.051 × 10⁹⁷(98-digit number)
30519848624124432237…91098338180448128001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.103 × 10⁹⁷(98-digit number)
61039697248248864474…82196676360896256001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.220 × 10⁹⁸(99-digit number)
12207939449649772894…64393352721792512001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.441 × 10⁹⁸(99-digit number)
24415878899299545789…28786705443585024001
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:57,909,467 XPM·at block #6,833,160 · updates every 60s
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