XPM Prime Explorer symbol
XPMPrime Explorer

Block #265,945

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/20/2013, 1:12:41 AM Β· Difficulty 9.9613 Β· 6,545,112 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a84cd5f424daa0cd44ed8de954e3234c034a7396fcd4962d21c80b5305c73153
View on Chainz β†—

Height

#265,945

Difficulty

9.961257

Transactions

2

Size

1.54 KB

Version

2

Bits

09f614e9

Nonce

500,134

Timestamp

11/20/2013, 1:12:41 AM

Confirmations

6,545,112

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c6b4c7fb98c946a75c7e6b01d37ce502c60ad4a27bdb4441777aa5589c3e8e55
Transactions (2)
Coinbase90a9885a876505…92859d1c1d8f82
1 in β†’ 1 out10.0897 XPM110 B
AeKNrjNj…1NEq95Ta
e24100e0784d65…7cfcfbf5556087
9 in β†’ 1 out3.0400 XPM1.35 KB
ASyL3JZF…2Mf9V5tj
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.

4.728 Γ— 10⁹¹(92-digit number)
47285156638313737852…09847315677432222109
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
4.728 Γ— 10⁹¹(92-digit number)
47285156638313737852…09847315677432222109
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.457 Γ— 10⁹¹(92-digit number)
94570313276627475704…19694631354864444219
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.891 Γ— 10⁹²(93-digit number)
18914062655325495140…39389262709728888439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.782 Γ— 10⁹²(93-digit number)
37828125310650990281…78778525419457776879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.565 Γ— 10⁹²(93-digit number)
75656250621301980563…57557050838915553759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.513 Γ— 10⁹³(94-digit number)
15131250124260396112…15114101677831107519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.026 Γ— 10⁹³(94-digit number)
30262500248520792225…30228203355662215039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.052 Γ— 10⁹³(94-digit number)
60525000497041584451…60456406711324430079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.210 Γ— 10⁹⁴(95-digit number)
12105000099408316890…20912813422648860159
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:57,732,560 XPMΒ·at block #6,811,056 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