Block #2,628,236

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/24/2018, 7:08:46 PM · Difficulty 11.2002 · 4,214,688 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0c81f5f26e5c1919b7b2ed8ae84936c016e4cc572c562598d8a5ba4f9fd72a79

Height

#2,628,236

Difficulty

11.200207

Transactions

59

Size

15.45 KB

Version

2

Bits

0b3340cb

Nonce

1,513,028,290

Timestamp

4/24/2018, 7:08:46 PM

Confirmations

4,214,688

Merkle Root

80d90c02e8479f9db72169e482ced392a8fce2e3fcdf8bbfa4f05f4a862a149a
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.

5.238 × 10⁹⁶(97-digit number)
52386505650517172857…04685474831565466241
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
5.238 × 10⁹⁶(97-digit number)
52386505650517172857…04685474831565466241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.047 × 10⁹⁷(98-digit number)
10477301130103434571…09370949663130932481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.095 × 10⁹⁷(98-digit number)
20954602260206869142…18741899326261864961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.190 × 10⁹⁷(98-digit number)
41909204520413738285…37483798652523729921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.381 × 10⁹⁷(98-digit number)
83818409040827476571…74967597305047459841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.676 × 10⁹⁸(99-digit number)
16763681808165495314…49935194610094919681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.352 × 10⁹⁸(99-digit number)
33527363616330990628…99870389220189839361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.705 × 10⁹⁸(99-digit number)
67054727232661981257…99740778440379678721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.341 × 10⁹⁹(100-digit number)
13410945446532396251…99481556880759357441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.682 × 10⁹⁹(100-digit number)
26821890893064792502…98963113761518714881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.364 × 10⁹⁹(100-digit number)
53643781786129585005…97926227523037429761
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:57,987,740 XPM·at block #6,842,923 · updates every 60s
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