Block #1,065,325

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/18/2015, 8:55:36 PM · Difficulty 10.7319 · 5,741,560 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
103f69e72988608b1eded1c281c44dce7337d98dfaf175fe5eb72f8e3852b2c7

Height

#1,065,325

Difficulty

10.731870

Transactions

2

Size

2.04 KB

Version

2

Bits

0abb5bda

Nonce

147,289,197

Timestamp

5/18/2015, 8:55:36 PM

Confirmations

5,741,560

Merkle Root

9e2272613a90a168099f160f27266434698469c6a9f52e675a9542ed1b269f00
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.

1.824 × 10⁹⁶(97-digit number)
18241735072558611226…25979337939895755519
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
1.824 × 10⁹⁶(97-digit number)
18241735072558611226…25979337939895755519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.648 × 10⁹⁶(97-digit number)
36483470145117222452…51958675879791511039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.296 × 10⁹⁶(97-digit number)
72966940290234444905…03917351759583022079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.459 × 10⁹⁷(98-digit number)
14593388058046888981…07834703519166044159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.918 × 10⁹⁷(98-digit number)
29186776116093777962…15669407038332088319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.837 × 10⁹⁷(98-digit number)
58373552232187555924…31338814076664176639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.167 × 10⁹⁸(99-digit number)
11674710446437511184…62677628153328353279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.334 × 10⁹⁸(99-digit number)
23349420892875022369…25355256306656706559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.669 × 10⁹⁸(99-digit number)
46698841785750044739…50710512613313413119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.339 × 10⁹⁸(99-digit number)
93397683571500089478…01421025226626826239
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:57,699,189 XPM·at block #6,806,884 · updates every 60s
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