Block #992,871

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/27/2015, 1:58:59 PM · Difficulty 10.8459 · 5,825,033 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9ea323da31f8f5fa868e7cfe693b8db4f553094f9a05c200108cbbe7a31b9872

Height

#992,871

Difficulty

10.845855

Transactions

2

Size

724 B

Version

2

Bits

0ad889f0

Nonce

403,325,764

Timestamp

3/27/2015, 1:58:59 PM

Confirmations

5,825,033

Merkle Root

fea271056ad2ce6cb2779d4f0e0500a8839201ba6317a7ceb10f6e6b8fae3a3f
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.

1.259 × 10⁹⁵(96-digit number)
12595129256499504898…96281478049203722239
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
1.259 × 10⁹⁵(96-digit number)
12595129256499504898…96281478049203722239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.519 × 10⁹⁵(96-digit number)
25190258512999009797…92562956098407444479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.038 × 10⁹⁵(96-digit number)
50380517025998019595…85125912196814888959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.007 × 10⁹⁶(97-digit number)
10076103405199603919…70251824393629777919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.015 × 10⁹⁶(97-digit number)
20152206810399207838…40503648787259555839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.030 × 10⁹⁶(97-digit number)
40304413620798415676…81007297574519111679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.060 × 10⁹⁶(97-digit number)
80608827241596831353…62014595149038223359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.612 × 10⁹⁷(98-digit number)
16121765448319366270…24029190298076446719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.224 × 10⁹⁷(98-digit number)
32243530896638732541…48058380596152893439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.448 × 10⁹⁷(98-digit number)
64487061793277465082…96116761192305786879
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:57,787,295 XPM·at block #6,817,903 · updates every 60s
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