XPM Prime Explorer symbol
XPMPrime Explorer

Block #284,349

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2013, 3:37:10 AM Β· Difficulty 9.9826 Β· 6,510,453 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
348292600e6661d21c5292d084ece9da4eb4e994290f35c0af56adde312f5123
View on Chainz β†—

Height

#284,349

Difficulty

9.982561

Transactions

2

Size

724 B

Version

2

Bits

09fb8916

Nonce

93,355

Timestamp

11/30/2013, 3:37:10 AM

Confirmations

6,510,453

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c51a9f60123bea5442ecb991f01e4c2e9b9b55116c81a3fdf281b992b3e2ae3c
Transactions (2)
Coinbase69ccb09c5a1e46…0490f54ac5287c
1 in β†’ 1 out10.0300 XPM110 B
AeKNrjNj…1NEq95Ta
8ca26018cbc918…6bfe5b5b17969d
3 in β†’ 2 out80.7569 XPM523 B
AKhr9iK6…mx9T9fjAARaKUszz…E5BYtrFM
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.

7.129 Γ— 10⁹⁢(97-digit number)
71292437794422354820…10179803081041773441
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
7.129 Γ— 10⁹⁢(97-digit number)
71292437794422354820…10179803081041773441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.425 Γ— 10⁹⁷(98-digit number)
14258487558884470964…20359606162083546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.851 Γ— 10⁹⁷(98-digit number)
28516975117768941928…40719212324167093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.703 Γ— 10⁹⁷(98-digit number)
57033950235537883856…81438424648334187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.140 Γ— 10⁹⁸(99-digit number)
11406790047107576771…62876849296668375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.281 Γ— 10⁹⁸(99-digit number)
22813580094215153542…25753698593336750081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.562 Γ— 10⁹⁸(99-digit number)
45627160188430307084…51507397186673500161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.125 Γ— 10⁹⁸(99-digit number)
91254320376860614169…03014794373347000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.825 Γ— 10⁹⁹(100-digit number)
18250864075372122833…06029588746694000641
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,602,469 XPMΒ·at block #6,794,801 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