Block #2,094,189

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/30/2017, 10:59:50 AM · Difficulty 10.8715 · 4,718,121 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cc809d6464ef73d8a6e311d54820030438b0d62db44d8747a88ef856415632fc

Height

#2,094,189

Difficulty

10.871538

Transactions

4

Size

2.30 KB

Version

2

Bits

0adf1d1c

Nonce

89,654,564

Timestamp

4/30/2017, 10:59:50 AM

Confirmations

4,718,121

Merkle Root

bc88fdeb2fd4d5039dd09c1a1f26dc91e8a89d3254f7c26a23e1cf1767e6235c
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.

2.422 × 10⁹³(94-digit number)
24227944580365725739…85347870206532666201
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
2.422 × 10⁹³(94-digit number)
24227944580365725739…85347870206532666201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.845 × 10⁹³(94-digit number)
48455889160731451478…70695740413065332401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.691 × 10⁹³(94-digit number)
96911778321462902957…41391480826130664801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.938 × 10⁹⁴(95-digit number)
19382355664292580591…82782961652261329601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.876 × 10⁹⁴(95-digit number)
38764711328585161183…65565923304522659201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.752 × 10⁹⁴(95-digit number)
77529422657170322366…31131846609045318401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.550 × 10⁹⁵(96-digit number)
15505884531434064473…62263693218090636801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.101 × 10⁹⁵(96-digit number)
31011769062868128946…24527386436181273601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.202 × 10⁹⁵(96-digit number)
62023538125736257892…49054772872362547201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.240 × 10⁹⁶(97-digit number)
12404707625147251578…98109545744725094401
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:57,742,494 XPM·at block #6,812,309 · updates every 60s
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