XPM Prime Explorer symbol
XPMPrime Explorer

Block #94,496

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/3/2013, 3:20:50 AM Β· Difficulty 9.2038 Β· 6,722,672 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9745c3099f020f66220950a42d28b5961fbfb15986842c711f45e8566c4e6e32
View on Chainz β†—

Height

#94,496

Difficulty

9.203769

Transactions

1

Size

200 B

Version

2

Bits

09342a30

Nonce

233,346

Timestamp

8/3/2013, 3:20:50 AM

Confirmations

6,722,672

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

02cd24608a654da6141862de1e2f3c9e6e4ffc78f39f7746110efc591edda569
Transactions (1)
Coinbase02cd24608a654d…0efc591edda569
1 in β†’ 1 out11.7900 XPM109 B
AXvMMum1…y1ajpFRb
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.

6.323 Γ— 10⁹⁷(98-digit number)
63233495953674457313…13494633404262819699
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
6.323 Γ— 10⁹⁷(98-digit number)
63233495953674457313…13494633404262819699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁸(99-digit number)
12646699190734891462…26989266808525639399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.529 Γ— 10⁹⁸(99-digit number)
25293398381469782925…53978533617051278799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.058 Γ— 10⁹⁸(99-digit number)
50586796762939565850…07957067234102557599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁹(100-digit number)
10117359352587913170…15914134468205115199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.023 Γ— 10⁹⁹(100-digit number)
20234718705175826340…31828268936410230399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.046 Γ— 10⁹⁹(100-digit number)
40469437410351652680…63656537872820460799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.093 Γ— 10⁹⁹(100-digit number)
80938874820703305361…27313075745640921599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.618 Γ— 10¹⁰⁰(101-digit number)
16187774964140661072…54626151491281843199
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:57,781,378 XPMΒ·at block #6,817,167 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.
Privacy PolicyΒ·
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