Block #1,352,928

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/3/2015, 9:22:51 PM · Difficulty 10.7962 · 5,452,162 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0c94d6bc9de647332af5392f2dd75fb1acbb29c205d698fc58666689fae9eb48

Height

#1,352,928

Difficulty

10.796231

Transactions

2

Size

1.72 KB

Version

2

Bits

0acbd5ce

Nonce

1,958,480,724

Timestamp

12/3/2015, 9:22:51 PM

Confirmations

5,452,162

Merkle Root

b2b825175a2a91d5e70099eaf542b10b633d5d9d2a9d9965476ff9bf83646946
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.

2.314 × 10⁹³(94-digit number)
23144656415547777550…17151014913038440799
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
2.314 × 10⁹³(94-digit number)
23144656415547777550…17151014913038440799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.628 × 10⁹³(94-digit number)
46289312831095555101…34302029826076881599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.257 × 10⁹³(94-digit number)
92578625662191110203…68604059652153763199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.851 × 10⁹⁴(95-digit number)
18515725132438222040…37208119304307526399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.703 × 10⁹⁴(95-digit number)
37031450264876444081…74416238608615052799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.406 × 10⁹⁴(95-digit number)
74062900529752888163…48832477217230105599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.481 × 10⁹⁵(96-digit number)
14812580105950577632…97664954434460211199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.962 × 10⁹⁵(96-digit number)
29625160211901155265…95329908868920422399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.925 × 10⁹⁵(96-digit number)
59250320423802310530…90659817737840844799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.185 × 10⁹⁶(97-digit number)
11850064084760462106…81319635475681689599
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:57,684,785 XPM·at block #6,805,089 · updates every 60s
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