Block #912,773

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2015, 4:22:22 AM · Difficulty 10.9283 · 5,896,949 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0ea9e24621c4d0c71c6a6ef07b44a1a6d2a6babbe2e408a1383181e01d453a11

Height

#912,773

Difficulty

10.928276

Transactions

4

Size

1.44 KB

Version

2

Bits

0aeda384

Nonce

2,069,426,470

Timestamp

1/28/2015, 4:22:22 AM

Confirmations

5,896,949

Merkle Root

4f5257b27e40c3713a8f43e1ede9aeba6bef10d59d956aa09db03c576298e7ea
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.

4.352 × 10⁹⁶(97-digit number)
43525897585715516540…73960951185417881599
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
4.352 × 10⁹⁶(97-digit number)
43525897585715516540…73960951185417881599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.705 × 10⁹⁶(97-digit number)
87051795171431033080…47921902370835763199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.741 × 10⁹⁷(98-digit number)
17410359034286206616…95843804741671526399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.482 × 10⁹⁷(98-digit number)
34820718068572413232…91687609483343052799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.964 × 10⁹⁷(98-digit number)
69641436137144826464…83375218966686105599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.392 × 10⁹⁸(99-digit number)
13928287227428965292…66750437933372211199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.785 × 10⁹⁸(99-digit number)
27856574454857930585…33500875866744422399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.571 × 10⁹⁸(99-digit number)
55713148909715861171…67001751733488844799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.114 × 10⁹⁹(100-digit number)
11142629781943172234…34003503466977689599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.228 × 10⁹⁹(100-digit number)
22285259563886344468…68007006933955379199
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:57,721,857 XPM·at block #6,809,721 · updates every 60s
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