XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #361,382

Block #361,382

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/16/2014, 1:10:35 AM Β· Difficulty 10.4043 Β· 6,451,109 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb44e610864ce0a389cd1e08b2da7a103bc70a962501ebce51838959464ccab5
View on Chainz β†—

Height

#361,382

Difficulty

10.404313

Transactions

1

Size

200 B

Version

2

Bits

0a678107

Nonce

17,450

Timestamp

1/16/2014, 1:10:35 AM

Confirmations

6,451,109

Merkle Root

af23ae9914154f7f626fd8bdf353525202a2a060a581f7bd59cf6727f824aa04
Transactions (1)
Coinbaseaf23ae9914154f…cf6727f824aa04
1 in β†’ 1 out9.2200 XPM109 B
AYJkXzMd…mL9i77Fz
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.

3.076 Γ— 10⁹⁷(98-digit number)
30767995252796898880…38860547199376005440
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
3.076 Γ— 10⁹⁷(98-digit number)
30767995252796898880…38860547199376005441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.153 Γ— 10⁹⁷(98-digit number)
61535990505593797760…77721094398752010881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.230 Γ— 10⁹⁸(99-digit number)
12307198101118759552…55442188797504021761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.461 Γ— 10⁹⁸(99-digit number)
24614396202237519104…10884377595008043521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.922 Γ— 10⁹⁸(99-digit number)
49228792404475038208…21768755190016087041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.845 Γ— 10⁹⁸(99-digit number)
98457584808950076416…43537510380032174081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.969 Γ— 10⁹⁹(100-digit number)
19691516961790015283…87075020760064348161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.938 Γ— 10⁹⁹(100-digit number)
39383033923580030566…74150041520128696321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.876 Γ— 10⁹⁹(100-digit number)
78766067847160061132…48300083040257392641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.575 Γ— 10¹⁰⁰(101-digit number)
15753213569432012226…96600166080514785281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 361382

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock cb44e610864ce0a389cd1e08b2da7a103bc70a962501ebce51838959464ccab5

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #361,382 on Chainz β†—
Circulating Supply:57,743,958 XPMΒ·at block #6,812,490 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