Block #632,813

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/14/2014, 11:19:03 AM · Difficulty 10.9631 · 6,172,194 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dcf8244a02d349808142cfb2da49687d3971e9b368ed5982d6452beb1d426a37

Height

#632,813

Difficulty

10.963083

Transactions

2

Size

433 B

Version

2

Bits

0af68c94

Nonce

1,576,606,970

Timestamp

7/14/2014, 11:19:03 AM

Confirmations

6,172,194

Merkle Root

150687f675ff383ef5da848f9efd786e2eeb26688246e58753d2a948a99d6df6
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.

3.774 × 10⁹⁷(98-digit number)
37741192934265195680…65387307322839190081
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
3.774 × 10⁹⁷(98-digit number)
37741192934265195680…65387307322839190081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.548 × 10⁹⁷(98-digit number)
75482385868530391361…30774614645678380161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.509 × 10⁹⁸(99-digit number)
15096477173706078272…61549229291356760321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.019 × 10⁹⁸(99-digit number)
30192954347412156544…23098458582713520641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.038 × 10⁹⁸(99-digit number)
60385908694824313088…46196917165427041281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.207 × 10⁹⁹(100-digit number)
12077181738964862617…92393834330854082561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.415 × 10⁹⁹(100-digit number)
24154363477929725235…84787668661708165121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.830 × 10⁹⁹(100-digit number)
48308726955859450471…69575337323416330241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.661 × 10⁹⁹(100-digit number)
96617453911718900942…39150674646832660481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.932 × 10¹⁰⁰(101-digit number)
19323490782343780188…78301349293665320961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.864 × 10¹⁰⁰(101-digit number)
38646981564687560376…56602698587330641921
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,684,125 XPM·at block #6,805,006 · updates every 60s
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