Block #360,175

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/15/2014, 7:02:14 AM · Difficulty 10.3889 · 6,444,987 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
125043f9dd6d261697831abf38e281a7eec70e5c2ba1c3b342025ab2002b99f1

Height

#360,175

Difficulty

10.388938

Transactions

1

Size

732 B

Version

2

Bits

0a63916c

Nonce

2,477

Timestamp

1/15/2014, 7:02:14 AM

Confirmations

6,444,987

Merkle Root

f496478be8ccbed4e09c787cf3737c1f12841529bc59f0d0b52bf327e2c11d0c
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.

1.191 × 10⁹⁶(97-digit number)
11917092356161099132…89258515878540851201
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
1.191 × 10⁹⁶(97-digit number)
11917092356161099132…89258515878540851201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.383 × 10⁹⁶(97-digit number)
23834184712322198264…78517031757081702401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.766 × 10⁹⁶(97-digit number)
47668369424644396528…57034063514163404801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.533 × 10⁹⁶(97-digit number)
95336738849288793057…14068127028326809601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.906 × 10⁹⁷(98-digit number)
19067347769857758611…28136254056653619201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.813 × 10⁹⁷(98-digit number)
38134695539715517222…56272508113307238401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.626 × 10⁹⁷(98-digit number)
76269391079431034445…12545016226614476801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.525 × 10⁹⁸(99-digit number)
15253878215886206889…25090032453228953601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.050 × 10⁹⁸(99-digit number)
30507756431772413778…50180064906457907201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.101 × 10⁹⁸(99-digit number)
61015512863544827556…00360129812915814401
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:57,685,363 XPM·at block #6,805,161 · updates every 60s
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