Block #2,650,602

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/6/2018, 4:27:24 AM · Difficulty 11.7556 · 4,180,637 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9ccb88c11186c432e3fe44d650f42eb96c339a7d03fcb16c4a95569dfa78247a

Height

#2,650,602

Difficulty

11.755639

Transactions

4

Size

1.98 KB

Version

2

Bits

0bc17194

Nonce

1,021,995,249

Timestamp

5/6/2018, 4:27:24 AM

Confirmations

4,180,637

Merkle Root

fa67e42c2853245d1c576af946804f6230cbcf5262dcf1378f7af19de078fd82
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.

3.278 × 10⁹⁵(96-digit number)
32784524493452284414…89840115257592796159
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
3.278 × 10⁹⁵(96-digit number)
32784524493452284414…89840115257592796159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.556 × 10⁹⁵(96-digit number)
65569048986904568828…79680230515185592319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.311 × 10⁹⁶(97-digit number)
13113809797380913765…59360461030371184639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.622 × 10⁹⁶(97-digit number)
26227619594761827531…18720922060742369279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.245 × 10⁹⁶(97-digit number)
52455239189523655063…37441844121484738559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.049 × 10⁹⁷(98-digit number)
10491047837904731012…74883688242969477119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.098 × 10⁹⁷(98-digit number)
20982095675809462025…49767376485938954239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.196 × 10⁹⁷(98-digit number)
41964191351618924050…99534752971877908479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.392 × 10⁹⁷(98-digit number)
83928382703237848100…99069505943755816959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.678 × 10⁹⁸(99-digit number)
16785676540647569620…98139011887511633919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.357 × 10⁹⁸(99-digit number)
33571353081295139240…96278023775023267839
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:57,894,061 XPM·at block #6,831,238 · updates every 60s
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