XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #329,091

Block #329,091

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/25/2013, 5:36:41 PM Β· Difficulty 10.1709 Β· 6,469,537 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
83921e594e4b350c81c98d3b4be06e0f6ba281fe211f00df58c85f085d216570
View on Chainz β†—

Height

#329,091

Difficulty

10.170877

Transactions

1

Size

206 B

Version

2

Bits

0a2bbe93

Nonce

137,040

Timestamp

12/25/2013, 5:36:41 PM

Confirmations

6,469,537

Merkle Root

74a459a1daa7545ef17d8defeee844bed12a547ed16b668b3417fcc04d7b2186
Transactions (1)
Coinbase74a459a1daa754…17fcc04d7b2186
1 in β†’ 1 out9.6500 XPM116 B
AbwWkWZt…kawDhufa
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.

1.006 Γ— 10⁹⁡(96-digit number)
10060033185016704244…12374247565644825600
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
1.006 Γ— 10⁹⁡(96-digit number)
10060033185016704244…12374247565644825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.012 Γ— 10⁹⁡(96-digit number)
20120066370033408489…24748495131289651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.024 Γ— 10⁹⁡(96-digit number)
40240132740066816978…49496990262579302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.048 Γ— 10⁹⁡(96-digit number)
80480265480133633957…98993980525158604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.609 Γ— 10⁹⁢(97-digit number)
16096053096026726791…97987961050317209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.219 Γ— 10⁹⁢(97-digit number)
32192106192053453583…95975922100634419199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.438 Γ— 10⁹⁢(97-digit number)
64384212384106907166…91951844201268838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.287 Γ— 10⁹⁷(98-digit number)
12876842476821381433…83903688402537676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.575 Γ— 10⁹⁷(98-digit number)
25753684953642762866…67807376805075353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.150 Γ— 10⁹⁷(98-digit number)
51507369907285525732…35614753610150707199
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 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.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 329091

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 83921e594e4b350c81c98d3b4be06e0f6ba281fe211f00df58c85f085d216570

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 #329,091 on Chainz β†—
Circulating Supply:57,633,043 XPMΒ·at block #6,798,627 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