Block #1,449,617

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2016, 6:26:33 PM · Difficulty 10.7536 · 5,377,034 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
084c6378f068408a06d6dd732cc20eb18a19fbdc9281a4c2d7fbc19bab99ec05

Height

#1,449,617

Difficulty

10.753604

Transactions

2

Size

3.34 KB

Version

2

Bits

0ac0ec33

Nonce

116,026

Timestamp

2/9/2016, 6:26:33 PM

Confirmations

5,377,034

Merkle Root

0eba873009b984e26357b9f064de27f13ee289ac6e6df70860b94d6ae0bb970c
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.

3.013 × 10¹⁰¹(102-digit number)
30130919565995758988…39525371211435417601
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
3.013 × 10¹⁰¹(102-digit number)
30130919565995758988…39525371211435417601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.026 × 10¹⁰¹(102-digit number)
60261839131991517976…79050742422870835201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.205 × 10¹⁰²(103-digit number)
12052367826398303595…58101484845741670401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.410 × 10¹⁰²(103-digit number)
24104735652796607190…16202969691483340801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.820 × 10¹⁰²(103-digit number)
48209471305593214381…32405939382966681601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.641 × 10¹⁰²(103-digit number)
96418942611186428762…64811878765933363201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.928 × 10¹⁰³(104-digit number)
19283788522237285752…29623757531866726401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.856 × 10¹⁰³(104-digit number)
38567577044474571505…59247515063733452801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.713 × 10¹⁰³(104-digit number)
77135154088949143010…18495030127466905601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.542 × 10¹⁰⁴(105-digit number)
15427030817789828602…36990060254933811201
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:57,857,357 XPM·at block #6,826,650 · updates every 60s
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