Block #2,887,119

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/19/2018, 1:24:31 AM · Difficulty 11.6209 · 3,944,323 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37ce1931247172e573d525a96cdba25083d0c531677f38d929d34f8be371ead9

Height

#2,887,119

Difficulty

11.620921

Transactions

7

Size

2.31 KB

Version

2

Bits

0b9ef4b3

Nonce

363,460,769

Timestamp

10/19/2018, 1:24:31 AM

Confirmations

3,944,323

Merkle Root

334a90a63e01803eff915009e0c68ab808567b3194c982ba943c81e1549f1373
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.

9.519 × 10⁹⁵(96-digit number)
95199870183579993515…86180260242911716001
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
9.519 × 10⁹⁵(96-digit number)
95199870183579993515…86180260242911716001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.903 × 10⁹⁶(97-digit number)
19039974036715998703…72360520485823432001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.807 × 10⁹⁶(97-digit number)
38079948073431997406…44721040971646864001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.615 × 10⁹⁶(97-digit number)
76159896146863994812…89442081943293728001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.523 × 10⁹⁷(98-digit number)
15231979229372798962…78884163886587456001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.046 × 10⁹⁷(98-digit number)
30463958458745597924…57768327773174912001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.092 × 10⁹⁷(98-digit number)
60927916917491195849…15536655546349824001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.218 × 10⁹⁸(99-digit number)
12185583383498239169…31073311092699648001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.437 × 10⁹⁸(99-digit number)
24371166766996478339…62146622185399296001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.874 × 10⁹⁸(99-digit number)
48742333533992956679…24293244370798592001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.748 × 10⁹⁸(99-digit number)
97484667067985913359…48586488741597184001
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,895,700 XPM·at block #6,831,441 · updates every 60s
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