Block #487,047

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 10:13:42 PM · Difficulty 10.6365 · 6,323,076 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
607b089fdcfc162017a32732eb805c8b8ae4b556bc9fbbc33b039d45fd1c285a

Height

#487,047

Difficulty

10.636533

Transactions

2

Size

730 B

Version

2

Bits

0aa2f3d0

Nonce

43,761,042

Timestamp

4/11/2014, 10:13:42 PM

Confirmations

6,323,076

Merkle Root

4be284177611a4e29e74b806a6c7290b6674b7f23c19b1102456d0687265f826
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.

1.798 × 10¹⁰⁰(101-digit number)
17985221041594872508…86784800679675197441
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
1.798 × 10¹⁰⁰(101-digit number)
17985221041594872508…86784800679675197441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.597 × 10¹⁰⁰(101-digit number)
35970442083189745016…73569601359350394881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.194 × 10¹⁰⁰(101-digit number)
71940884166379490033…47139202718700789761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.438 × 10¹⁰¹(102-digit number)
14388176833275898006…94278405437401579521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.877 × 10¹⁰¹(102-digit number)
28776353666551796013…88556810874803159041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.755 × 10¹⁰¹(102-digit number)
57552707333103592026…77113621749606318081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.151 × 10¹⁰²(103-digit number)
11510541466620718405…54227243499212636161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.302 × 10¹⁰²(103-digit number)
23021082933241436810…08454486998425272321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.604 × 10¹⁰²(103-digit number)
46042165866482873621…16908973996850544641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.208 × 10¹⁰²(103-digit number)
92084331732965747242…33817947993701089281
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:57,725,057 XPM·at block #6,810,122 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy