Block #1,102,545

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/13/2015, 8:48:41 AM · Difficulty 10.7587 · 5,703,607 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51fb8cb0410006e9bb0915f43378d9d04f5c692e8b76475d17197205782abd13

Height

#1,102,545

Difficulty

10.758687

Transactions

4

Size

877 B

Version

2

Bits

0ac23954

Nonce

129,080,976

Timestamp

6/13/2015, 8:48:41 AM

Confirmations

5,703,607

Merkle Root

9321d4e948899dc3e6269c5e6d399711ad7825d7d5c52d4282342acf738eb17d
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.

5.666 × 10⁹⁵(96-digit number)
56666998148792322015…62837191638463511039
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
5.666 × 10⁹⁵(96-digit number)
56666998148792322015…62837191638463511039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.133 × 10⁹⁶(97-digit number)
11333399629758464403…25674383276927022079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.266 × 10⁹⁶(97-digit number)
22666799259516928806…51348766553854044159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.533 × 10⁹⁶(97-digit number)
45333598519033857612…02697533107708088319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.066 × 10⁹⁶(97-digit number)
90667197038067715224…05395066215416176639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.813 × 10⁹⁷(98-digit number)
18133439407613543044…10790132430832353279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.626 × 10⁹⁷(98-digit number)
36266878815227086089…21580264861664706559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.253 × 10⁹⁷(98-digit number)
72533757630454172179…43160529723329413119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.450 × 10⁹⁸(99-digit number)
14506751526090834435…86321059446658826239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.901 × 10⁹⁸(99-digit number)
29013503052181668871…72642118893317652479
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:57,693,296 XPM·at block #6,806,151 · updates every 60s
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