Block #994,347

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/28/2015, 3:26:33 PM · Difficulty 10.8443 · 5,822,572 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1151a65edde0d402332a6d569f010653ab17263a7c6ce6fbea49d872c86c3b7f

Height

#994,347

Difficulty

10.844302

Transactions

2

Size

574 B

Version

2

Bits

0ad82427

Nonce

1,040,115,835

Timestamp

3/28/2015, 3:26:33 PM

Confirmations

5,822,572

Merkle Root

c06370cbe5bc8023ddf24dbf9be426823bc61fe9f22d2aa7979b782ce19e49ec
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.

4.289 × 10⁹⁶(97-digit number)
42893016595323586702…11071389057430010879
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
4.289 × 10⁹⁶(97-digit number)
42893016595323586702…11071389057430010879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.578 × 10⁹⁶(97-digit number)
85786033190647173405…22142778114860021759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.715 × 10⁹⁷(98-digit number)
17157206638129434681…44285556229720043519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.431 × 10⁹⁷(98-digit number)
34314413276258869362…88571112459440087039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.862 × 10⁹⁷(98-digit number)
68628826552517738724…77142224918880174079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.372 × 10⁹⁸(99-digit number)
13725765310503547744…54284449837760348159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.745 × 10⁹⁸(99-digit number)
27451530621007095489…08568899675520696319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.490 × 10⁹⁸(99-digit number)
54903061242014190979…17137799351041392639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.098 × 10⁹⁹(100-digit number)
10980612248402838195…34275598702082785279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.196 × 10⁹⁹(100-digit number)
21961224496805676391…68551197404165570559
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:57,779,394 XPM·at block #6,816,918 · updates every 60s
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