XPM Prime Explorer symbol
XPMPrime Explorer

Block #181,769

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2013, 7:15:48 PM Β· Difficulty 9.8603 Β· 6,619,692 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1e767267d307260a963b8445ed07152b6def7ea5881c9b69b239c3cffb3cd9f7
View on Chainz β†—

Height

#181,769

Difficulty

9.860265

Transactions

1

Size

199 B

Version

2

Bits

09dc3a55

Nonce

98,737

Timestamp

9/26/2013, 7:15:48 PM

Confirmations

6,619,692

Mined by

⛏️ P2SHAUm1UXE6PTt11eQB2DXhcmZJbwSTx2UrXW

Merkle Root

9654641370d390792cc7c812557db732f491500d108ab2d8143e457f0ff41825
Transactions (1)
Coinbase9654641370d390…3e457f0ff41825
1 in β†’ 1 out10.2700 XPM109 B
AUm1UXE6…STx2UrXW
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.712 Γ— 10⁹⁡(96-digit number)
27127969487239853879…58380394110476511999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.712 Γ— 10⁹⁡(96-digit number)
27127969487239853879…58380394110476511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.425 Γ— 10⁹⁡(96-digit number)
54255938974479707758…16760788220953023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.085 Γ— 10⁹⁢(97-digit number)
10851187794895941551…33521576441906047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.170 Γ— 10⁹⁢(97-digit number)
21702375589791883103…67043152883812095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.340 Γ— 10⁹⁢(97-digit number)
43404751179583766206…34086305767624191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.680 Γ— 10⁹⁢(97-digit number)
86809502359167532413…68172611535248383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.736 Γ— 10⁹⁷(98-digit number)
17361900471833506482…36345223070496767999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.472 Γ— 10⁹⁷(98-digit number)
34723800943667012965…72690446140993535999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.944 Γ— 10⁹⁷(98-digit number)
69447601887334025930…45380892281987071999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,655,762 XPMΒ·at block #6,801,460 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK