Block #2,633,482

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/28/2018, 11:20:05 AM · Difficulty 11.1931 · 4,197,810 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4118515d865a4d45b8fb6cdbed1a0f8986647dc4e499d28de2d61dd3c4ff4301

Height

#2,633,482

Difficulty

11.193061

Transactions

3

Size

802 B

Version

2

Bits

0b316c76

Nonce

795,677,931

Timestamp

4/28/2018, 11:20:05 AM

Confirmations

4,197,810

Merkle Root

0b8ef23f6918e10ba355bd34a8693ebaf5a37bfb966703b02a910d2b336361b6
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.

7.697 × 10⁹⁶(97-digit number)
76973042283388594845…83486007940797090559
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
7.697 × 10⁹⁶(97-digit number)
76973042283388594845…83486007940797090559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.539 × 10⁹⁷(98-digit number)
15394608456677718969…66972015881594181119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.078 × 10⁹⁷(98-digit number)
30789216913355437938…33944031763188362239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.157 × 10⁹⁷(98-digit number)
61578433826710875876…67888063526376724479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.231 × 10⁹⁸(99-digit number)
12315686765342175175…35776127052753448959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.463 × 10⁹⁸(99-digit number)
24631373530684350350…71552254105506897919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.926 × 10⁹⁸(99-digit number)
49262747061368700701…43104508211013795839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.852 × 10⁹⁸(99-digit number)
98525494122737401402…86209016422027591679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.970 × 10⁹⁹(100-digit number)
19705098824547480280…72418032844055183359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.941 × 10⁹⁹(100-digit number)
39410197649094960561…44836065688110366719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.882 × 10⁹⁹(100-digit number)
78820395298189921122…89672131376220733439
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:57,894,482 XPM·at block #6,831,291 · updates every 60s
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