Block #2,644,126

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/2/2018, 8:55:56 AM · Difficulty 11.7026 · 4,189,367 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
167c00bb507fe7fe5dc41d6cb08516d49f7c9616de6b65c444c7e1cd029db7ef

Height

#2,644,126

Difficulty

11.702649

Transactions

2

Size

721 B

Version

2

Bits

0bb3e0cd

Nonce

386,682,474

Timestamp

5/2/2018, 8:55:56 AM

Confirmations

4,189,367

Merkle Root

7ae2a1aa0d5d5d3d7ddea0c09e25063065ba8cf16ff87c888ab16c798134cad4
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.

2.262 × 10⁹³(94-digit number)
22629583696204228388…94614911484358868239
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
2.262 × 10⁹³(94-digit number)
22629583696204228388…94614911484358868239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.525 × 10⁹³(94-digit number)
45259167392408456777…89229822968717736479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.051 × 10⁹³(94-digit number)
90518334784816913555…78459645937435472959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.810 × 10⁹⁴(95-digit number)
18103666956963382711…56919291874870945919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.620 × 10⁹⁴(95-digit number)
36207333913926765422…13838583749741891839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.241 × 10⁹⁴(95-digit number)
72414667827853530844…27677167499483783679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.448 × 10⁹⁵(96-digit number)
14482933565570706168…55354334998967567359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.896 × 10⁹⁵(96-digit number)
28965867131141412337…10708669997935134719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.793 × 10⁹⁵(96-digit number)
57931734262282824675…21417339995870269439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.158 × 10⁹⁶(97-digit number)
11586346852456564935…42834679991740538879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.317 × 10⁹⁶(97-digit number)
23172693704913129870…85669359983481077759
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:57,912,148 XPM·at block #6,833,492 · updates every 60s
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