XPM Prime Explorer symbol
XPMPrime Explorer

Block #146,209

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2013, 9:03:17 AM Β· Difficulty 9.8469 Β· 6,665,595 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
558ea30045610130114c2814034b3487483e40a139c368dc03e3a9207d0d3bf2
View on Chainz β†—

Height

#146,209

Difficulty

9.846877

Transactions

1

Size

198 B

Version

2

Bits

09d8ccf6

Nonce

10,445

Timestamp

9/2/2013, 9:03:17 AM

Confirmations

6,665,595

Mined by

⛏️ P2SHAKaGDwVVv7VLKh2cmLacAjw2bVh5Bk5GFu

Merkle Root

3105e933e6234b2f1ffddbf4272dcb58a34e3c7d3dd918cef6ceee3f0a6b32e2
Transactions (1)
Coinbase3105e933e6234b…ceee3f0a6b32e2
1 in β†’ 1 out10.3000 XPM109 B
AKaGDwVV…h5Bk5GFu
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.

3.362 Γ— 10⁹³(94-digit number)
33622878034936206063…95974821501752755199
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
3.362 Γ— 10⁹³(94-digit number)
33622878034936206063…95974821501752755199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.724 Γ— 10⁹³(94-digit number)
67245756069872412126…91949643003505510399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.344 Γ— 10⁹⁴(95-digit number)
13449151213974482425…83899286007011020799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.689 Γ— 10⁹⁴(95-digit number)
26898302427948964850…67798572014022041599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.379 Γ— 10⁹⁴(95-digit number)
53796604855897929700…35597144028044083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.075 Γ— 10⁹⁡(96-digit number)
10759320971179585940…71194288056088166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.151 Γ— 10⁹⁡(96-digit number)
21518641942359171880…42388576112176332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.303 Γ— 10⁹⁡(96-digit number)
43037283884718343760…84777152224352665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.607 Γ— 10⁹⁡(96-digit number)
86074567769436687521…69554304448705331199
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:57,738,529 XPMΒ·at block #6,811,803 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

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy