Block #2,094,194

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/30/2017, 11:03:22 AM · Difficulty 10.8715 · 4,718,383 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
647f26e09af173e3aa34c37ff4b03a1c1b0501b31344d383e43d89f156beb478

Height

#2,094,194

Difficulty

10.871502

Transactions

4

Size

879 B

Version

2

Bits

0adf1ab9

Nonce

385,031,485

Timestamp

4/30/2017, 11:03:22 AM

Confirmations

4,718,383

Merkle Root

dbaae182a72d0379918222bd0041957c9d98e6c94f85a71243da7cff75dccb58
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.

1.468 × 10⁹⁶(97-digit number)
14685359763932828194…79456489394974300161
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
1.468 × 10⁹⁶(97-digit number)
14685359763932828194…79456489394974300161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.937 × 10⁹⁶(97-digit number)
29370719527865656389…58912978789948600321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.874 × 10⁹⁶(97-digit number)
58741439055731312778…17825957579897200641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.174 × 10⁹⁷(98-digit number)
11748287811146262555…35651915159794401281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.349 × 10⁹⁷(98-digit number)
23496575622292525111…71303830319588802561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.699 × 10⁹⁷(98-digit number)
46993151244585050222…42607660639177605121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.398 × 10⁹⁷(98-digit number)
93986302489170100445…85215321278355210241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.879 × 10⁹⁸(99-digit number)
18797260497834020089…70430642556710420481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.759 × 10⁹⁸(99-digit number)
37594520995668040178…40861285113420840961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.518 × 10⁹⁸(99-digit number)
75189041991336080356…81722570226841681921
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:57,744,650 XPM·at block #6,812,576 · updates every 60s
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