Block #2,683,119

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/29/2018, 2:43:27 PM · Difficulty 11.6901 · 4,158,461 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
085104f4779cd3e8a0d06e21265406ac0c88ed0d7b08d76994b13873c67ee19b

Height

#2,683,119

Difficulty

11.690082

Transactions

36

Size

8.85 KB

Version

2

Bits

0bb0a93e

Nonce

1,509,004,004

Timestamp

5/29/2018, 2:43:27 PM

Confirmations

4,158,461

Merkle Root

0ec87b4cde8e69a81f802c0b1dc6a2ea2a3907b91f53dea884814e9551cb8a14
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.

1.402 × 10⁹⁷(98-digit number)
14020657148600054996…33920148450665123839
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
1.402 × 10⁹⁷(98-digit number)
14020657148600054996…33920148450665123839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.804 × 10⁹⁷(98-digit number)
28041314297200109992…67840296901330247679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.608 × 10⁹⁷(98-digit number)
56082628594400219984…35680593802660495359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.121 × 10⁹⁸(99-digit number)
11216525718880043996…71361187605320990719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.243 × 10⁹⁸(99-digit number)
22433051437760087993…42722375210641981439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.486 × 10⁹⁸(99-digit number)
44866102875520175987…85444750421283962879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.973 × 10⁹⁸(99-digit number)
89732205751040351975…70889500842567925759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.794 × 10⁹⁹(100-digit number)
17946441150208070395…41779001685135851519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.589 × 10⁹⁹(100-digit number)
35892882300416140790…83558003370271703039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.178 × 10⁹⁹(100-digit number)
71785764600832281580…67116006740543406079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.435 × 10¹⁰⁰(101-digit number)
14357152920166456316…34232013481086812159
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:57,977,026 XPM·at block #6,841,579 · updates every 60s
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