Block #1,370,227

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/15/2015, 12:03:33 PM · Difficulty 10.8191 · 5,438,200 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5692865f9c08fa03a4acbfaf6f1bf473c3a4ec6945f65eab7c5a91a3ee9306b9

Height

#1,370,227

Difficulty

10.819149

Transactions

2

Size

10.96 KB

Version

2

Bits

0ad1b3c5

Nonce

734,469,094

Timestamp

12/15/2015, 12:03:33 PM

Confirmations

5,438,200

Merkle Root

e1770da62d9152fd9182e07b32fcc3d8884214dfadde75947bab41c96446b98f
Transactions (2)
1 in → 1 out8.6800 XPM110 B
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.

1.760 × 10⁹⁵(96-digit number)
17609897376946619016…32840002262857870001
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
1.760 × 10⁹⁵(96-digit number)
17609897376946619016…32840002262857870001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.521 × 10⁹⁵(96-digit number)
35219794753893238033…65680004525715740001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.043 × 10⁹⁵(96-digit number)
70439589507786476066…31360009051431480001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.408 × 10⁹⁶(97-digit number)
14087917901557295213…62720018102862960001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.817 × 10⁹⁶(97-digit number)
28175835803114590426…25440036205725920001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.635 × 10⁹⁶(97-digit number)
56351671606229180853…50880072411451840001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.127 × 10⁹⁷(98-digit number)
11270334321245836170…01760144822903680001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.254 × 10⁹⁷(98-digit number)
22540668642491672341…03520289645807360001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.508 × 10⁹⁷(98-digit number)
45081337284983344682…07040579291614720001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.016 × 10⁹⁷(98-digit number)
90162674569966689365…14081158583229440001
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:57,711,476 XPM·at block #6,808,426 · updates every 60s
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