Block #1,924,066

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/4/2017, 9:54:36 PM · Difficulty 10.7202 · 4,907,394 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
822c80184c690cf92d16672e972ddd7e8e999183a1e28703e299806024f381e5

Height

#1,924,066

Difficulty

10.720201

Transactions

2

Size

574 B

Version

2

Bits

0ab85f1d

Nonce

1,745,990,278

Timestamp

1/4/2017, 9:54:36 PM

Confirmations

4,907,394

Merkle Root

d678b995f97eb8e9d25e2e53f391a5526af751f441243caec9a1566a4d55ab0b
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.

1.289 × 10⁹⁵(96-digit number)
12890183429112563841…84422824856748557439
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
1.289 × 10⁹⁵(96-digit number)
12890183429112563841…84422824856748557439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.578 × 10⁹⁵(96-digit number)
25780366858225127682…68845649713497114879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.156 × 10⁹⁵(96-digit number)
51560733716450255364…37691299426994229759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.031 × 10⁹⁶(97-digit number)
10312146743290051072…75382598853988459519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.062 × 10⁹⁶(97-digit number)
20624293486580102145…50765197707976919039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.124 × 10⁹⁶(97-digit number)
41248586973160204291…01530395415953838079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.249 × 10⁹⁶(97-digit number)
82497173946320408583…03060790831907676159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.649 × 10⁹⁷(98-digit number)
16499434789264081716…06121581663815352319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.299 × 10⁹⁷(98-digit number)
32998869578528163433…12243163327630704639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.599 × 10⁹⁷(98-digit number)
65997739157056326867…24486326655261409279
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:57,895,771 XPM·at block #6,831,459 · updates every 60s
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