Block #2,885,225

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/17/2018, 4:48:54 PM · Difficulty 11.6255 · 3,955,036 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
60aca65da1d83d8297053b272ed8cfd76106d9b85a98346a4305bcc56b4bc05f

Height

#2,885,225

Difficulty

11.625508

Transactions

3

Size

949 B

Version

2

Bits

0ba02143

Nonce

1,440,462,072

Timestamp

10/17/2018, 4:48:54 PM

Confirmations

3,955,036

Merkle Root

39375b1243988362e96edf32de26851ff33d27af4d907b2eab79393d5a001906
Transactions (3)
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.

1.561 × 10⁹⁶(97-digit number)
15610575884480050781…50421541433242076801
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
1.561 × 10⁹⁶(97-digit number)
15610575884480050781…50421541433242076801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.122 × 10⁹⁶(97-digit number)
31221151768960101563…00843082866484153601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.244 × 10⁹⁶(97-digit number)
62442303537920203126…01686165732968307201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.248 × 10⁹⁷(98-digit number)
12488460707584040625…03372331465936614401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.497 × 10⁹⁷(98-digit number)
24976921415168081250…06744662931873228801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.995 × 10⁹⁷(98-digit number)
49953842830336162501…13489325863746457601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.990 × 10⁹⁷(98-digit number)
99907685660672325003…26978651727492915201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.998 × 10⁹⁸(99-digit number)
19981537132134465000…53957303454985830401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.996 × 10⁹⁸(99-digit number)
39963074264268930001…07914606909971660801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.992 × 10⁹⁸(99-digit number)
79926148528537860002…15829213819943321601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.598 × 10⁹⁹(100-digit number)
15985229705707572000…31658427639886643201
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:57,966,401 XPM·at block #6,840,260 · updates every 60s
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