Block #1,073,766

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/24/2015, 2:49:04 PM · Difficulty 10.7408 · 5,741,089 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a3da1681145ee465fd2473c98aaa3f8d93ff0525546336b7406104e9012e3e0d

Height

#1,073,766

Difficulty

10.740806

Transactions

2

Size

868 B

Version

2

Bits

0abda576

Nonce

1,312,337,277

Timestamp

5/24/2015, 2:49:04 PM

Confirmations

5,741,089

Merkle Root

16870db64b5e652c56ea25fd6c5599d5f19448a1bc732b355a43a35b205bcf07
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.

2.769 × 10⁹⁷(98-digit number)
27698470488494509461…37853337180027996161
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
2.769 × 10⁹⁷(98-digit number)
27698470488494509461…37853337180027996161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.539 × 10⁹⁷(98-digit number)
55396940976989018923…75706674360055992321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.107 × 10⁹⁸(99-digit number)
11079388195397803784…51413348720111984641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.215 × 10⁹⁸(99-digit number)
22158776390795607569…02826697440223969281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.431 × 10⁹⁸(99-digit number)
44317552781591215138…05653394880447938561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.863 × 10⁹⁸(99-digit number)
88635105563182430277…11306789760895877121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.772 × 10⁹⁹(100-digit number)
17727021112636486055…22613579521791754241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.545 × 10⁹⁹(100-digit number)
35454042225272972110…45227159043583508481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.090 × 10⁹⁹(100-digit number)
70908084450545944221…90454318087167016961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.418 × 10¹⁰⁰(101-digit number)
14181616890109188844…80908636174334033921
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,762,923 XPM·at block #6,814,854 · updates every 60s
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