Block #487,865

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/12/2014, 9:45:50 AM · Difficulty 10.6457 · 6,317,319 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6d4b38ac7c0e72b5111078e26f4e23079884a1ba7ec7d8c3d7412b6cdd9e5306

Height

#487,865

Difficulty

10.645668

Transactions

4

Size

1.39 KB

Version

2

Bits

0aa54a86

Nonce

14,643

Timestamp

4/12/2014, 9:45:50 AM

Confirmations

6,317,319

Merkle Root

f6fd0b490280328ed471023d7332b2a744dc151fae4c5e549753deaee36dd671
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.

5.971 × 10¹⁰⁵(106-digit number)
59711211206534064176…45197134226005440001
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
5.971 × 10¹⁰⁵(106-digit number)
59711211206534064176…45197134226005440001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.194 × 10¹⁰⁶(107-digit number)
11942242241306812835…90394268452010880001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.388 × 10¹⁰⁶(107-digit number)
23884484482613625670…80788536904021760001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.776 × 10¹⁰⁶(107-digit number)
47768968965227251341…61577073808043520001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.553 × 10¹⁰⁶(107-digit number)
95537937930454502682…23154147616087040001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.910 × 10¹⁰⁷(108-digit number)
19107587586090900536…46308295232174080001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.821 × 10¹⁰⁷(108-digit number)
38215175172181801072…92616590464348160001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.643 × 10¹⁰⁷(108-digit number)
76430350344363602145…85233180928696320001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.528 × 10¹⁰⁸(109-digit number)
15286070068872720429…70466361857392640001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.057 × 10¹⁰⁸(109-digit number)
30572140137745440858…40932723714785280001
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:57,685,542 XPM·at block #6,805,183 · updates every 60s
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