Block #247,030

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/6/2013, 12:37:51 PM · Difficulty 9.9645 · 6,594,172 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f81c1cf5dd6ff9d9e094a91a345c3563c36a1f776cbf092b0f21d61e289b4991

Height

#247,030

Difficulty

9.964537

Transactions

1

Size

1.74 KB

Version

2

Bits

09f6ebe3

Nonce

120,584

Timestamp

11/6/2013, 12:37:51 PM

Confirmations

6,594,172

Merkle Root

244ef33691c89f0635d19ef274cb078e7a9a56c99b26bb984868c48bbb406414
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.

1.608 × 10⁹¹(92-digit number)
16085177855953994398…64190920510395660801
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
1.608 × 10⁹¹(92-digit number)
16085177855953994398…64190920510395660801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.217 × 10⁹¹(92-digit number)
32170355711907988797…28381841020791321601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.434 × 10⁹¹(92-digit number)
64340711423815977594…56763682041582643201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.286 × 10⁹²(93-digit number)
12868142284763195518…13527364083165286401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.573 × 10⁹²(93-digit number)
25736284569526391037…27054728166330572801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.147 × 10⁹²(93-digit number)
51472569139052782075…54109456332661145601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.029 × 10⁹³(94-digit number)
10294513827810556415…08218912665322291201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.058 × 10⁹³(94-digit number)
20589027655621112830…16437825330644582401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.117 × 10⁹³(94-digit number)
41178055311242225660…32875650661289164801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.235 × 10⁹³(94-digit number)
82356110622484451320…65751301322578329601
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:57,973,977 XPM·at block #6,841,201 · updates every 60s
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