Block #485,880

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 7:39:24 AM · Difficulty 10.6147 · 6,310,639 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2acc98d9249a48cd9c586267b1b9d6dc8cdaec65fcefcb6e0b6c730d5a9e27b1

Height

#485,880

Difficulty

10.614734

Transactions

4

Size

1.58 KB

Version

2

Bits

0a9d5f2f

Nonce

227,888

Timestamp

4/11/2014, 7:39:24 AM

Confirmations

6,310,639

Merkle Root

fcd08dcb289e552d5753116dc07c16bb3d36c0f0456952f42fcba675a6c740f8
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.

1.227 × 10⁹⁹(100-digit number)
12275103066178330829…19485068459086906401
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
1.227 × 10⁹⁹(100-digit number)
12275103066178330829…19485068459086906401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.455 × 10⁹⁹(100-digit number)
24550206132356661658…38970136918173812801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.910 × 10⁹⁹(100-digit number)
49100412264713323317…77940273836347625601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.820 × 10⁹⁹(100-digit number)
98200824529426646635…55880547672695251201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.964 × 10¹⁰⁰(101-digit number)
19640164905885329327…11761095345390502401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.928 × 10¹⁰⁰(101-digit number)
39280329811770658654…23522190690781004801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.856 × 10¹⁰⁰(101-digit number)
78560659623541317308…47044381381562009601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.571 × 10¹⁰¹(102-digit number)
15712131924708263461…94088762763124019201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.142 × 10¹⁰¹(102-digit number)
31424263849416526923…88177525526248038401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.284 × 10¹⁰¹(102-digit number)
62848527698833053846…76355051052496076801
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:57,616,149 XPM·at block #6,796,518 · updates every 60s
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