Block #487,502

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/12/2014, 4:39:11 AM · Difficulty 10.6418 · 6,325,191 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1014f73f6c477da2dcd21a4b7ffb306dbbc8466822bb52e5ff17ac72e208f009

Height

#487,502

Difficulty

10.641807

Transactions

2

Size

433 B

Version

2

Bits

0aa44d76

Nonce

7,619

Timestamp

4/12/2014, 4:39:11 AM

Confirmations

6,325,191

Merkle Root

c35a4075dfbfe49f0b83556521a96f935c9f1a5f8de8c2871758d73c38852721
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.

8.281 × 10⁹⁶(97-digit number)
82816503981037168516…89353288188518517381
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
8.281 × 10⁹⁶(97-digit number)
82816503981037168516…89353288188518517381
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.656 × 10⁹⁷(98-digit number)
16563300796207433703…78706576377037034761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.312 × 10⁹⁷(98-digit number)
33126601592414867406…57413152754074069521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.625 × 10⁹⁷(98-digit number)
66253203184829734813…14826305508148139041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.325 × 10⁹⁸(99-digit number)
13250640636965946962…29652611016296278081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.650 × 10⁹⁸(99-digit number)
26501281273931893925…59305222032592556161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.300 × 10⁹⁸(99-digit number)
53002562547863787850…18610444065185112321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.060 × 10⁹⁹(100-digit number)
10600512509572757570…37220888130370224641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.120 × 10⁹⁹(100-digit number)
21201025019145515140…74441776260740449281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.240 × 10⁹⁹(100-digit number)
42402050038291030280…48883552521480898561
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:57,745,579 XPM·at block #6,812,692 · updates every 60s
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