Block #1,063,738

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/17/2015, 7:21:07 PM · Difficulty 10.7290 · 5,744,993 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f05db803b876898aa35fbaea75247efadbb22e7abbe02e531ffe7ef82b15b13

Height

#1,063,738

Difficulty

10.728966

Transactions

5

Size

1.66 KB

Version

2

Bits

0aba9d87

Nonce

112,511,717

Timestamp

5/17/2015, 7:21:07 PM

Confirmations

5,744,993

Merkle Root

1fb91a4f958a7e9333a745f3902ab4cb5806a39b8578ac176bb51a3a3080e31a
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.

7.086 × 10⁹⁶(97-digit number)
70863353755570851818…89450730175036682879
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
7.086 × 10⁹⁶(97-digit number)
70863353755570851818…89450730175036682879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.417 × 10⁹⁷(98-digit number)
14172670751114170363…78901460350073365759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.834 × 10⁹⁷(98-digit number)
28345341502228340727…57802920700146731519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.669 × 10⁹⁷(98-digit number)
56690683004456681454…15605841400293463039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.133 × 10⁹⁸(99-digit number)
11338136600891336290…31211682800586926079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.267 × 10⁹⁸(99-digit number)
22676273201782672581…62423365601173852159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.535 × 10⁹⁸(99-digit number)
45352546403565345163…24846731202347704319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.070 × 10⁹⁸(99-digit number)
90705092807130690327…49693462404695408639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.814 × 10⁹⁹(100-digit number)
18141018561426138065…99386924809390817279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.628 × 10⁹⁹(100-digit number)
36282037122852276131…98773849618781634559
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:57,713,894 XPM·at block #6,808,730 · updates every 60s
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