Block #2,455,011

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/3/2018, 2:15:06 AM · Difficulty 10.9523 · 4,384,602 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9eab570cd7c7f773d0fccfd330e752edf3d405c3811d1e964ae41241f9d0e118

Height

#2,455,011

Difficulty

10.952320

Transactions

5

Size

1.55 KB

Version

2

Bits

0af3cb3b

Nonce

1,175,524,091

Timestamp

1/3/2018, 2:15:06 AM

Confirmations

4,384,602

Merkle Root

2d3106bee2cf4216953ecdf1733304d0983f2e76223cedb00396ffbe18c74e45
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.

2.322 × 10⁹⁵(96-digit number)
23227386529913157255…88265053362245672961
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
2.322 × 10⁹⁵(96-digit number)
23227386529913157255…88265053362245672961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.645 × 10⁹⁵(96-digit number)
46454773059826314510…76530106724491345921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.290 × 10⁹⁵(96-digit number)
92909546119652629020…53060213448982691841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.858 × 10⁹⁶(97-digit number)
18581909223930525804…06120426897965383681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.716 × 10⁹⁶(97-digit number)
37163818447861051608…12240853795930767361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.432 × 10⁹⁶(97-digit number)
74327636895722103216…24481707591861534721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.486 × 10⁹⁷(98-digit number)
14865527379144420643…48963415183723069441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.973 × 10⁹⁷(98-digit number)
29731054758288841286…97926830367446138881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.946 × 10⁹⁷(98-digit number)
59462109516577682573…95853660734892277761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.189 × 10⁹⁸(99-digit number)
11892421903315536514…91707321469784555521
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:57,961,194 XPM·at block #6,839,612 · updates every 60s
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