Block #1,264,312

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/2/2015, 7:10:20 PM · Difficulty 10.8227 · 5,562,531 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8e01402bbaf193eba55336638b91c7ea47986b4bb6b78956d4bf6c6c89b0d319

Height

#1,264,312

Difficulty

10.822665

Transactions

2

Size

571 B

Version

2

Bits

0ad29a2e

Nonce

409,136,487

Timestamp

10/2/2015, 7:10:20 PM

Confirmations

5,562,531

Merkle Root

bcc9a1ed94cced41c4af618673fc97019e904eda2e0e4d4bfddfb743febed9e3
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.

5.217 × 10⁹²(93-digit number)
52179169083898594489…24228142448561978561
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
5.217 × 10⁹²(93-digit number)
52179169083898594489…24228142448561978561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.043 × 10⁹³(94-digit number)
10435833816779718897…48456284897123957121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.087 × 10⁹³(94-digit number)
20871667633559437795…96912569794247914241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.174 × 10⁹³(94-digit number)
41743335267118875591…93825139588495828481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.348 × 10⁹³(94-digit number)
83486670534237751183…87650279176991656961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.669 × 10⁹⁴(95-digit number)
16697334106847550236…75300558353983313921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.339 × 10⁹⁴(95-digit number)
33394668213695100473…50601116707966627841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.678 × 10⁹⁴(95-digit number)
66789336427390200946…01202233415933255681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.335 × 10⁹⁵(96-digit number)
13357867285478040189…02404466831866511361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.671 × 10⁹⁵(96-digit number)
26715734570956080378…04808933663733022721
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:57,858,909 XPM·at block #6,826,842 · updates every 60s
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