Block #933,508

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/12/2015, 5:10:00 PM · Difficulty 10.9016 · 5,873,127 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5f11ba070edb98a61e71a98a664d40ec83415f306be5f3675ab3132e50c22d86

Height

#933,508

Difficulty

10.901647

Transactions

2

Size

877 B

Version

2

Bits

0ae6d250

Nonce

272,204,296

Timestamp

2/12/2015, 5:10:00 PM

Confirmations

5,873,127

Merkle Root

3d7f837000fe95e2c684097b3c03d1e038a69286fb2e1477c92a3006592b6f91
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.

2.001 × 10⁹⁸(99-digit number)
20016000846256146017…20098233224542054401
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
2.001 × 10⁹⁸(99-digit number)
20016000846256146017…20098233224542054401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.003 × 10⁹⁸(99-digit number)
40032001692512292034…40196466449084108801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.006 × 10⁹⁸(99-digit number)
80064003385024584069…80392932898168217601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.601 × 10⁹⁹(100-digit number)
16012800677004916813…60785865796336435201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.202 × 10⁹⁹(100-digit number)
32025601354009833627…21571731592672870401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.405 × 10⁹⁹(100-digit number)
64051202708019667255…43143463185345740801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.281 × 10¹⁰⁰(101-digit number)
12810240541603933451…86286926370691481601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.562 × 10¹⁰⁰(101-digit number)
25620481083207866902…72573852741382963201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.124 × 10¹⁰⁰(101-digit number)
51240962166415733804…45147705482765926401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.024 × 10¹⁰¹(102-digit number)
10248192433283146760…90295410965531852801
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:57,697,174 XPM·at block #6,806,634 · 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