Block #794,538

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/2/2014, 11:32:15 PM · Difficulty 10.9750 · 6,020,411 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de3c72cdb70c5ff4a3c7fd34b375100f431ff154832c5f24e9d54c04b280edfe

Height

#794,538

Difficulty

10.974986

Transactions

4

Size

1.30 KB

Version

2

Bits

0af998b7

Nonce

3,044,656,969

Timestamp

11/2/2014, 11:32:15 PM

Confirmations

6,020,411

Merkle Root

2daa51b81c3d320cb0dedf7252b119925500497b086286fa4e22b8741e2d0de8
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.

2.808 × 10⁹⁸(99-digit number)
28082121299742077961…73478357947114639361
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
2.808 × 10⁹⁸(99-digit number)
28082121299742077961…73478357947114639361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.616 × 10⁹⁸(99-digit number)
56164242599484155923…46956715894229278721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.123 × 10⁹⁹(100-digit number)
11232848519896831184…93913431788458557441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.246 × 10⁹⁹(100-digit number)
22465697039793662369…87826863576917114881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.493 × 10⁹⁹(100-digit number)
44931394079587324738…75653727153834229761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.986 × 10⁹⁹(100-digit number)
89862788159174649477…51307454307668459521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.797 × 10¹⁰⁰(101-digit number)
17972557631834929895…02614908615336919041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.594 × 10¹⁰⁰(101-digit number)
35945115263669859791…05229817230673838081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.189 × 10¹⁰⁰(101-digit number)
71890230527339719582…10459634461347676161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.437 × 10¹⁰¹(102-digit number)
14378046105467943916…20919268922695352321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.875 × 10¹⁰¹(102-digit number)
28756092210935887832…41838537845390704641
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:57,763,689 XPM·at block #6,814,948 · updates every 60s
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