Block #2,630,977

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/26/2018, 7:37:52 PM · Difficulty 11.1732 · 4,211,132 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4c5241810b99ebad561eaeef1affe6c9dc227e358213360ca397bef9a7b4d522

Height

#2,630,977

Difficulty

11.173205

Transactions

52

Size

15.25 KB

Version

2

Bits

0b2c572e

Nonce

572,955,719

Timestamp

4/26/2018, 7:37:52 PM

Confirmations

4,211,132

Merkle Root

1aa20aa535ac96f5a005f819e1d4aad0d064737e23ad780c06e8f1c2ed30bafa
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.

5.988 × 10⁹⁵(96-digit number)
59884015843560876753…00440734268364517119
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
5.988 × 10⁹⁵(96-digit number)
59884015843560876753…00440734268364517119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.197 × 10⁹⁶(97-digit number)
11976803168712175350…00881468536729034239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.395 × 10⁹⁶(97-digit number)
23953606337424350701…01762937073458068479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.790 × 10⁹⁶(97-digit number)
47907212674848701402…03525874146916136959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.581 × 10⁹⁶(97-digit number)
95814425349697402805…07051748293832273919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.916 × 10⁹⁷(98-digit number)
19162885069939480561…14103496587664547839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.832 × 10⁹⁷(98-digit number)
38325770139878961122…28206993175329095679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.665 × 10⁹⁷(98-digit number)
76651540279757922244…56413986350658191359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.533 × 10⁹⁸(99-digit number)
15330308055951584448…12827972701316382719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.066 × 10⁹⁸(99-digit number)
30660616111903168897…25655945402632765439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
6.132 × 10⁹⁸(99-digit number)
61321232223806337795…51311890805265530879
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:57,981,260 XPM·at block #6,842,108 · updates every 60s
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