Block #2,875,979

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 10/10/2018, 11:05:18 PM · Difficulty 11.6577 · 3,960,572 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
57e23562ac4091a28418999e226fc9529a45467cb2a620d876d05ffa2f109826

Height

#2,875,979

Difficulty

11.657665

Transactions

5

Size

1.16 KB

Version

2

Bits

0ba85cc4

Nonce

1,341,572,172

Timestamp

10/10/2018, 11:05:18 PM

Confirmations

3,960,572

Merkle Root

0e4bfa65f0c1830dd777a200f80f3c1028f15a0bc86bf5d76852938dc163c9b0
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.

3.809 × 10⁹⁶(97-digit number)
38099186920275875741…95985412723886613439
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
3.809 × 10⁹⁶(97-digit number)
38099186920275875741…95985412723886613439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.619 × 10⁹⁶(97-digit number)
76198373840551751482…91970825447773226879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.523 × 10⁹⁷(98-digit number)
15239674768110350296…83941650895546453759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.047 × 10⁹⁷(98-digit number)
30479349536220700593…67883301791092907519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.095 × 10⁹⁷(98-digit number)
60958699072441401186…35766603582185815039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.219 × 10⁹⁸(99-digit number)
12191739814488280237…71533207164371630079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.438 × 10⁹⁸(99-digit number)
24383479628976560474…43066414328743260159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.876 × 10⁹⁸(99-digit number)
48766959257953120948…86132828657486520319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.753 × 10⁹⁸(99-digit number)
97533918515906241897…72265657314973040639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.950 × 10⁹⁹(100-digit number)
19506783703181248379…44531314629946081279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.901 × 10⁹⁹(100-digit number)
39013567406362496759…89062629259892162559
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,936,673 XPM·at block #6,836,550 · updates every 60s
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