Block #1,066,056

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/19/2015, 7:47:14 AM · Difficulty 10.7361 · 5,741,554 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
177e37150a01e736f8484a6d07508a4f4c6e3a812e2c1734ce2be567c02af281

Height

#1,066,056

Difficulty

10.736078

Transactions

3

Size

660 B

Version

2

Bits

0abc6f9d

Nonce

594,681,488

Timestamp

5/19/2015, 7:47:14 AM

Confirmations

5,741,554

Merkle Root

d6f58e79091bb562d2b6a8ecde33700bc0faa069f461f06e46500849ca58b1c7
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.

5.811 × 10⁹⁷(98-digit number)
58119813744864558832…47385392235092530561
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
5.811 × 10⁹⁷(98-digit number)
58119813744864558832…47385392235092530561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.162 × 10⁹⁸(99-digit number)
11623962748972911766…94770784470185061121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.324 × 10⁹⁸(99-digit number)
23247925497945823533…89541568940370122241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.649 × 10⁹⁸(99-digit number)
46495850995891647066…79083137880740244481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.299 × 10⁹⁸(99-digit number)
92991701991783294132…58166275761480488961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.859 × 10⁹⁹(100-digit number)
18598340398356658826…16332551522960977921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.719 × 10⁹⁹(100-digit number)
37196680796713317652…32665103045921955841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.439 × 10⁹⁹(100-digit number)
74393361593426635305…65330206091843911681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.487 × 10¹⁰⁰(101-digit number)
14878672318685327061…30660412183687823361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.975 × 10¹⁰⁰(101-digit number)
29757344637370654122…61320824367375646721
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:57,704,910 XPM·at block #6,807,609 · updates every 60s
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