Block #487,929

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/12/2014, 10:35:09 AM · Difficulty 10.6466 · 6,315,856 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8e9c1a32667ddd446777f26d0516553dc4b8d6d714fcb5f12c7e3ba8724782e2

Height

#487,929

Difficulty

10.646611

Transactions

2

Size

616 B

Version

2

Bits

0aa58854

Nonce

71,974,137

Timestamp

4/12/2014, 10:35:09 AM

Confirmations

6,315,856

Merkle Root

41dbe19d45fc243fa5d67ff4c5e0b07e337b447df440eb5dcc4a2ca4e39b71d9
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.

4.876 × 10⁹⁸(99-digit number)
48761047145002905233…18158705315942385601
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
4.876 × 10⁹⁸(99-digit number)
48761047145002905233…18158705315942385601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.752 × 10⁹⁸(99-digit number)
97522094290005810466…36317410631884771201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.950 × 10⁹⁹(100-digit number)
19504418858001162093…72634821263769542401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.900 × 10⁹⁹(100-digit number)
39008837716002324186…45269642527539084801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.801 × 10⁹⁹(100-digit number)
78017675432004648372…90539285055078169601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.560 × 10¹⁰⁰(101-digit number)
15603535086400929674…81078570110156339201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.120 × 10¹⁰⁰(101-digit number)
31207070172801859349…62157140220312678401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.241 × 10¹⁰⁰(101-digit number)
62414140345603718698…24314280440625356801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.248 × 10¹⁰¹(102-digit number)
12482828069120743739…48628560881250713601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.496 × 10¹⁰¹(102-digit number)
24965656138241487479…97257121762501427201
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:57,674,320 XPM·at block #6,803,784 · 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.