Block #2,929,768

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/19/2018, 9:07:19 AM · Difficulty 11.3851 · 3,912,781 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2aabe2d1ab8c693ec1541665031f3c85e9e727b3afe01117f9b894bf58fc347e

Height

#2,929,768

Difficulty

11.385128

Transactions

2

Size

870 B

Version

2

Bits

0b6297c7

Nonce

422,932,408

Timestamp

11/19/2018, 9:07:19 AM

Confirmations

3,912,781

Merkle Root

6589410d7fa9826703f8a791f5c9c61dd9733a26520e92cfa0a0fd49e7c81424
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.

2.882 × 10⁹⁵(96-digit number)
28820131359019400763…12789765038076613761
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
2.882 × 10⁹⁵(96-digit number)
28820131359019400763…12789765038076613761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.764 × 10⁹⁵(96-digit number)
57640262718038801527…25579530076153227521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.152 × 10⁹⁶(97-digit number)
11528052543607760305…51159060152306455041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.305 × 10⁹⁶(97-digit number)
23056105087215520610…02318120304612910081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.611 × 10⁹⁶(97-digit number)
46112210174431041221…04636240609225820161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.222 × 10⁹⁶(97-digit number)
92224420348862082443…09272481218451640321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.844 × 10⁹⁷(98-digit number)
18444884069772416488…18544962436903280641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.688 × 10⁹⁷(98-digit number)
36889768139544832977…37089924873806561281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.377 × 10⁹⁷(98-digit number)
73779536279089665954…74179849747613122561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.475 × 10⁹⁸(99-digit number)
14755907255817933190…48359699495226245121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.951 × 10⁹⁸(99-digit number)
29511814511635866381…96719398990452490241
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:57,984,817 XPM·at block #6,842,548 · updates every 60s
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