XPM Prime Explorer symbol
XPMPrime Explorer

Block #241,065

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/2/2013, 11:40:39 PM Β· Difficulty 9.9576 Β· 6,576,614 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
db4f359e1527d74400f08049251974c62fcb43718bbcd911c1841385dd716a9c
View on Chainz β†—

Height

#241,065

Difficulty

9.957568

Transactions

1

Size

199 B

Version

2

Bits

09f52325

Nonce

85,529

Timestamp

11/2/2013, 11:40:39 PM

Confirmations

6,576,614

Mined by

⛏️ P2SHAHNdTz9RdyhMpsaRttP7HwiXvgDHU2jpcA

Merkle Root

41f4c8a26ad4f2b066cc54baaf13735a4d738a74878c6152277c767b46ce7d2e
Transactions (1)
Coinbase41f4c8a26ad4f2…7c767b46ce7d2e
1 in β†’ 1 out10.0700 XPM109 B
AHNdTz9R…DHU2jpcA
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.

6.444 Γ— 10⁹³(94-digit number)
64440295017882147136…21048924399382755199
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
6.444 Γ— 10⁹³(94-digit number)
64440295017882147136…21048924399382755199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.288 Γ— 10⁹⁴(95-digit number)
12888059003576429427…42097848798765510399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.577 Γ— 10⁹⁴(95-digit number)
25776118007152858854…84195697597531020799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.155 Γ— 10⁹⁴(95-digit number)
51552236014305717709…68391395195062041599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.031 Γ— 10⁹⁡(96-digit number)
10310447202861143541…36782790390124083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.062 Γ— 10⁹⁡(96-digit number)
20620894405722287083…73565580780248166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.124 Γ— 10⁹⁡(96-digit number)
41241788811444574167…47131161560496332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.248 Γ— 10⁹⁡(96-digit number)
82483577622889148334…94262323120992665599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.649 Γ— 10⁹⁢(97-digit number)
16496715524577829666…88524646241985331199
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:57,785,489 XPMΒ·at block #6,817,678 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