Block #1,080,062

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/28/2015, 4:13:03 PM · Difficulty 10.7633 · 5,727,005 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
824065920c05a9f63d93c02001ccdbaa73b35909dac7ce4ebfe393164dc66c52

Height

#1,080,062

Difficulty

10.763312

Transactions

1

Size

243 B

Version

2

Bits

0ac36864

Nonce

491,566,680

Timestamp

5/28/2015, 4:13:03 PM

Confirmations

5,727,005

Merkle Root

e4f3e11b61b4df42783c4c03e376ba17bf39842a45e5cfd0956662c4954900a9
Transactions (1)
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.

3.951 × 10⁹⁶(97-digit number)
39512383819921001033…34537197704401289601
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
3.951 × 10⁹⁶(97-digit number)
39512383819921001033…34537197704401289601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.902 × 10⁹⁶(97-digit number)
79024767639842002066…69074395408802579201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.580 × 10⁹⁷(98-digit number)
15804953527968400413…38148790817605158401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.160 × 10⁹⁷(98-digit number)
31609907055936800826…76297581635210316801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.321 × 10⁹⁷(98-digit number)
63219814111873601653…52595163270420633601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.264 × 10⁹⁸(99-digit number)
12643962822374720330…05190326540841267201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.528 × 10⁹⁸(99-digit number)
25287925644749440661…10380653081682534401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.057 × 10⁹⁸(99-digit number)
50575851289498881322…20761306163365068801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.011 × 10⁹⁹(100-digit number)
10115170257899776264…41522612326730137601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.023 × 10⁹⁹(100-digit number)
20230340515799552529…83045224653460275201
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:57,700,634 XPM·at block #6,807,066 · updates every 60s
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