Block #524,365

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/4/2014, 3:34:46 AM · Difficulty 10.8758 · 6,302,642 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
919d27bc1002a9c717131163dcb91386d415f72105c1f443f458797bb5b92c47

Height

#524,365

Difficulty

10.875822

Transactions

4

Size

1.44 KB

Version

2

Bits

0ae035e0

Nonce

361,812

Timestamp

5/4/2014, 3:34:46 AM

Confirmations

6,302,642

Merkle Root

6067cf10980c04df54c5e028af50a349a8c164485f2f969ed41abb9273c9c57e
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.

3.290 × 10⁹⁶(97-digit number)
32903287072082269069…01099799900032518549
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
3.290 × 10⁹⁶(97-digit number)
32903287072082269069…01099799900032518549
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.580 × 10⁹⁶(97-digit number)
65806574144164538139…02199599800065037099
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.316 × 10⁹⁷(98-digit number)
13161314828832907627…04399199600130074199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.632 × 10⁹⁷(98-digit number)
26322629657665815255…08798399200260148399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.264 × 10⁹⁷(98-digit number)
52645259315331630511…17596798400520296799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.052 × 10⁹⁸(99-digit number)
10529051863066326102…35193596801040593599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.105 × 10⁹⁸(99-digit number)
21058103726132652204…70387193602081187199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.211 × 10⁹⁸(99-digit number)
42116207452265304409…40774387204162374399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.423 × 10⁹⁸(99-digit number)
84232414904530608818…81548774408324748799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.684 × 10⁹⁹(100-digit number)
16846482980906121763…63097548816649497599
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:57,860,232 XPM·at block #6,827,006 · updates every 60s
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