Block #1,294,442

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/22/2015, 8:21:06 PM · Difficulty 10.8627 · 5,515,265 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e550ac8317d703b2784ee23e181bb7397d1eefc87cc2f65afddf572b36992e00

Height

#1,294,442

Difficulty

10.862675

Transactions

3

Size

798 B

Version

2

Bits

0adcd83e

Nonce

111,157,853

Timestamp

10/22/2015, 8:21:06 PM

Confirmations

5,515,265

Merkle Root

ea97ebc2bd53d8fe1f8deb0ba96be99d2390d1ee83906988742d47b9fa487f4c
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.

7.976 × 10⁹⁴(95-digit number)
79760770861489385210…94579214712162935841
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
7.976 × 10⁹⁴(95-digit number)
79760770861489385210…94579214712162935841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.595 × 10⁹⁵(96-digit number)
15952154172297877042…89158429424325871681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.190 × 10⁹⁵(96-digit number)
31904308344595754084…78316858848651743361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.380 × 10⁹⁵(96-digit number)
63808616689191508168…56633717697303486721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.276 × 10⁹⁶(97-digit number)
12761723337838301633…13267435394606973441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.552 × 10⁹⁶(97-digit number)
25523446675676603267…26534870789213946881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.104 × 10⁹⁶(97-digit number)
51046893351353206534…53069741578427893761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.020 × 10⁹⁷(98-digit number)
10209378670270641306…06139483156855787521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.041 × 10⁹⁷(98-digit number)
20418757340541282613…12278966313711575041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.083 × 10⁹⁷(98-digit number)
40837514681082565227…24557932627423150081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
8.167 × 10⁹⁷(98-digit number)
81675029362165130455…49115865254846300161
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:57,721,735 XPM·at block #6,809,706 · updates every 60s
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