Block #1,571,982

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/5/2016, 2:06:25 AM · Difficulty 10.7322 · 5,269,552 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
18efc3a2a46b16c8614dfc2fb88fe7145aaad8982701adc7b0e526c3b587df73

Height

#1,571,982

Difficulty

10.732203

Transactions

2

Size

833 B

Version

2

Bits

0abb71a9

Nonce

1,200,759,235

Timestamp

5/5/2016, 2:06:25 AM

Confirmations

5,269,552

Merkle Root

1d43f7339accb9873511060bb37d33bf547ef14e8471c48bac2fb09aef4d1534
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.

5.549 × 10⁹³(94-digit number)
55492735313205555345…85865765170623928301
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
5.549 × 10⁹³(94-digit number)
55492735313205555345…85865765170623928301
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.109 × 10⁹⁴(95-digit number)
11098547062641111069…71731530341247856601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.219 × 10⁹⁴(95-digit number)
22197094125282222138…43463060682495713201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.439 × 10⁹⁴(95-digit number)
44394188250564444276…86926121364991426401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.878 × 10⁹⁴(95-digit number)
88788376501128888552…73852242729982852801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.775 × 10⁹⁵(96-digit number)
17757675300225777710…47704485459965705601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.551 × 10⁹⁵(96-digit number)
35515350600451555420…95408970919931411201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.103 × 10⁹⁵(96-digit number)
71030701200903110841…90817941839862822401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.420 × 10⁹⁶(97-digit number)
14206140240180622168…81635883679725644801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.841 × 10⁹⁶(97-digit number)
28412280480361244336…63271767359451289601
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:57,976,655 XPM·at block #6,841,533 · updates every 60s
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