Block #1,885,419

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/9/2016, 2:14:34 AM · Difficulty 10.7171 · 4,957,607 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3be61df414b0903d693bec177414c28ea22763fcf0394f84bc1a8e344d55acfe

Height

#1,885,419

Difficulty

10.717121

Transactions

2

Size

572 B

Version

2

Bits

0ab7953d

Nonce

515,099,734

Timestamp

12/9/2016, 2:14:34 AM

Confirmations

4,957,607

Merkle Root

5c005eb5b9a3cd5ee7970a21556f2deb03aa5f1b397ff608688c3dab0b3eccd4
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.

6.774 × 10⁹¹(92-digit number)
67743779114637583675…63228850610955507099
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
6.774 × 10⁹¹(92-digit number)
67743779114637583675…63228850610955507099
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.354 × 10⁹²(93-digit number)
13548755822927516735…26457701221911014199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.709 × 10⁹²(93-digit number)
27097511645855033470…52915402443822028399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.419 × 10⁹²(93-digit number)
54195023291710066940…05830804887644056799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.083 × 10⁹³(94-digit number)
10839004658342013388…11661609775288113599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.167 × 10⁹³(94-digit number)
21678009316684026776…23323219550576227199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.335 × 10⁹³(94-digit number)
43356018633368053552…46646439101152454399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.671 × 10⁹³(94-digit number)
86712037266736107104…93292878202304908799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.734 × 10⁹⁴(95-digit number)
17342407453347221420…86585756404609817599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.468 × 10⁹⁴(95-digit number)
34684814906694442841…73171512809219635199
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,988,562 XPM·at block #6,843,025 · updates every 60s
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