Block #2,167,012

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/19/2017, 7:28:20 AM · Difficulty 10.8976 · 4,676,409 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c15d1e4b8339cb1d8ade464a1392e0ff9ef55cc4051a4724f0b5ae894284fe45

Height

#2,167,012

Difficulty

10.897610

Transactions

4

Size

2.16 KB

Version

2

Bits

0ae5c9bf

Nonce

1,584,634,964

Timestamp

6/19/2017, 7:28:20 AM

Confirmations

4,676,409

Merkle Root

6bac8fcd0b0a2ceb65f79dfdffe650d6cd5abc2adc744f93d61fbc94e379e259
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.

1.186 × 10⁹⁶(97-digit number)
11863186160492800999…79934240518812376321
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
1.186 × 10⁹⁶(97-digit number)
11863186160492800999…79934240518812376321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.372 × 10⁹⁶(97-digit number)
23726372320985601999…59868481037624752641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.745 × 10⁹⁶(97-digit number)
47452744641971203998…19736962075249505281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.490 × 10⁹⁶(97-digit number)
94905489283942407996…39473924150499010561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.898 × 10⁹⁷(98-digit number)
18981097856788481599…78947848300998021121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.796 × 10⁹⁷(98-digit number)
37962195713576963198…57895696601996042241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.592 × 10⁹⁷(98-digit number)
75924391427153926397…15791393203992084481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.518 × 10⁹⁸(99-digit number)
15184878285430785279…31582786407984168961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.036 × 10⁹⁸(99-digit number)
30369756570861570558…63165572815968337921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.073 × 10⁹⁸(99-digit number)
60739513141723141117…26331145631936675841
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:57,991,736 XPM·at block #6,843,420 · updates every 60s
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