Block #1,195,585

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/15/2015, 6:43:37 PM · Difficulty 10.8352 · 5,610,332 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2aca99fd259649fefefa3b7c49344c63bbd99eb12a7026d6e925553481e9ff60

Height

#1,195,585

Difficulty

10.835179

Transactions

5

Size

1.66 KB

Version

2

Bits

0ad5ce4b

Nonce

49,486,848

Timestamp

8/15/2015, 6:43:37 PM

Confirmations

5,610,332

Merkle Root

b4803eb6c0b92a2a941b8565f7ace2d7ed17f2ed47e931721d345873129a5261
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.

8.332 × 10⁹⁶(97-digit number)
83320522054311562332…23385433418113931521
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
8.332 × 10⁹⁶(97-digit number)
83320522054311562332…23385433418113931521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.666 × 10⁹⁷(98-digit number)
16664104410862312466…46770866836227863041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.332 × 10⁹⁷(98-digit number)
33328208821724624933…93541733672455726081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.665 × 10⁹⁷(98-digit number)
66656417643449249866…87083467344911452161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.333 × 10⁹⁸(99-digit number)
13331283528689849973…74166934689822904321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.666 × 10⁹⁸(99-digit number)
26662567057379699946…48333869379645808641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.332 × 10⁹⁸(99-digit number)
53325134114759399892…96667738759291617281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.066 × 10⁹⁹(100-digit number)
10665026822951879978…93335477518583234561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.133 × 10⁹⁹(100-digit number)
21330053645903759957…86670955037166469121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.266 × 10⁹⁹(100-digit number)
42660107291807519914…73341910074332938241
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:57,691,426 XPM·at block #6,805,916 · updates every 60s
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