Block #2,840,384

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/15/2018, 12:32:05 PM · Difficulty 11.7202 · 4,001,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
43d9374a23028e3cd667c41f24e3f9654f32d6c111bb2e2649593b8ad59b5226

Height

#2,840,384

Difficulty

11.720158

Transactions

3

Size

618 B

Version

2

Bits

0bb85c48

Nonce

152,616,775

Timestamp

9/15/2018, 12:32:05 PM

Confirmations

4,001,166

Merkle Root

9bc8c1e67e22f555675346b6ef357ca4e60ca4598ccd43f49e38d6661a5fbeb0
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.

1.424 × 10⁹⁷(98-digit number)
14246701928374693093…26884484170839121919
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
1.424 × 10⁹⁷(98-digit number)
14246701928374693093…26884484170839121919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.849 × 10⁹⁷(98-digit number)
28493403856749386187…53768968341678243839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.698 × 10⁹⁷(98-digit number)
56986807713498772375…07537936683356487679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.139 × 10⁹⁸(99-digit number)
11397361542699754475…15075873366712975359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.279 × 10⁹⁸(99-digit number)
22794723085399508950…30151746733425950719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.558 × 10⁹⁸(99-digit number)
45589446170799017900…60303493466851901439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.117 × 10⁹⁸(99-digit number)
91178892341598035800…20606986933703802879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.823 × 10⁹⁹(100-digit number)
18235778468319607160…41213973867407605759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.647 × 10⁹⁹(100-digit number)
36471556936639214320…82427947734815211519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.294 × 10⁹⁹(100-digit number)
72943113873278428640…64855895469630423039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.458 × 10¹⁰⁰(101-digit number)
14588622774655685728…29711790939260846079
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,976,784 XPM·at block #6,841,549 · updates every 60s
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