Block #1,183,891

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/5/2015, 7:35:08 PM · Difficulty 10.9023 · 5,658,680 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ad12176788e7aaa9d4084fa91ae7771a30fbe0d7663eb59fa8a99c7534bb3ee

Height

#1,183,891

Difficulty

10.902343

Transactions

3

Size

1.47 KB

Version

2

Bits

0ae6ffee

Nonce

147,768,398

Timestamp

8/5/2015, 7:35:08 PM

Confirmations

5,658,680

Merkle Root

3202c0a1028ad087dd52a151d25b740386f2200098d42f5f29b1805fefe1e018
Transactions (3)
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.

1.149 × 10⁹⁴(95-digit number)
11493344338265251624…29728163683154503681
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
1.149 × 10⁹⁴(95-digit number)
11493344338265251624…29728163683154503681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.298 × 10⁹⁴(95-digit number)
22986688676530503248…59456327366309007361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.597 × 10⁹⁴(95-digit number)
45973377353061006497…18912654732618014721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.194 × 10⁹⁴(95-digit number)
91946754706122012994…37825309465236029441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.838 × 10⁹⁵(96-digit number)
18389350941224402598…75650618930472058881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.677 × 10⁹⁵(96-digit number)
36778701882448805197…51301237860944117761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.355 × 10⁹⁵(96-digit number)
73557403764897610395…02602475721888235521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.471 × 10⁹⁶(97-digit number)
14711480752979522079…05204951443776471041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.942 × 10⁹⁶(97-digit number)
29422961505959044158…10409902887552942081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.884 × 10⁹⁶(97-digit number)
58845923011918088316…20819805775105884161
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:57,984,995 XPM·at block #6,842,570 · updates every 60s
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