Block #1,263,984

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/2/2015, 1:43:32 PM · Difficulty 10.8226 · 5,539,683 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
28e19b9c5e26c1b75cc33f2addc7d683a7c6f095bea666cdb6bea1154ec56f17

Height

#1,263,984

Difficulty

10.822642

Transactions

2

Size

427 B

Version

2

Bits

0ad298a9

Nonce

265,864,373

Timestamp

10/2/2015, 1:43:32 PM

Confirmations

5,539,683

Merkle Root

76e17225d06c26774054da4ce2bf50315adf7a2e9a5a4fe3a7463bdefff299a1
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.

4.679 × 10⁹⁶(97-digit number)
46792180352477033078…24629464509765365761
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
4.679 × 10⁹⁶(97-digit number)
46792180352477033078…24629464509765365761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.358 × 10⁹⁶(97-digit number)
93584360704954066156…49258929019530731521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.871 × 10⁹⁷(98-digit number)
18716872140990813231…98517858039061463041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.743 × 10⁹⁷(98-digit number)
37433744281981626462…97035716078122926081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.486 × 10⁹⁷(98-digit number)
74867488563963252925…94071432156245852161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.497 × 10⁹⁸(99-digit number)
14973497712792650585…88142864312491704321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.994 × 10⁹⁸(99-digit number)
29946995425585301170…76285728624983408641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.989 × 10⁹⁸(99-digit number)
59893990851170602340…52571457249966817281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.197 × 10⁹⁹(100-digit number)
11978798170234120468…05142914499933634561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.395 × 10⁹⁹(100-digit number)
23957596340468240936…10285828999867269121
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:57,673,372 XPM·at block #6,803,666 · updates every 60s
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