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Home/Chain Registry/Block #2,732,004

Block #2,732,004

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/3/2018, 4:28:23 AM Β· Difficulty 11.6311 Β· 4,112,052 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0739f8c6dd0d52609db96ea9f5d01c450b6eee64bf4d9f843a51cd20374c519d
View on Chainz β†—

Difficulty

11.631078

Transactions

1

Size

200 B

Version

2

Bits

0ba18e5c

Nonce

151,541,399

Timestamp

7/3/2018, 4:28:23 AM

Confirmations

4,112,052

Merkle Root

93995140e8b90a18c353b067fe2dc3374dd9f22b13b55d5fde289fe14d539f2c
Transactions (1)
Coinbase93995140e8b90a…289fe14d539f2c
1 in β†’ 1 out7.3800 XPM110 B
AH6MAK7g…19nXGRRx
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.

1.737 Γ— 10⁹⁴(95-digit number)
17370214526843359632…97616492298917955000
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
1.737 Γ— 10⁹⁴(95-digit number)
17370214526843359632…97616492298917955001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.474 Γ— 10⁹⁴(95-digit number)
34740429053686719265…95232984597835910001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.948 Γ— 10⁹⁴(95-digit number)
69480858107373438530…90465969195671820001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.389 Γ— 10⁹⁡(96-digit number)
13896171621474687706…80931938391343640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.779 Γ— 10⁹⁡(96-digit number)
27792343242949375412…61863876782687280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.558 Γ— 10⁹⁡(96-digit number)
55584686485898750824…23727753565374560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.111 Γ— 10⁹⁢(97-digit number)
11116937297179750164…47455507130749120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.223 Γ— 10⁹⁢(97-digit number)
22233874594359500329…94911014261498240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.446 Γ— 10⁹⁢(97-digit number)
44467749188719000659…89822028522996480001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.893 Γ— 10⁹⁢(97-digit number)
88935498377438001319…79644057045992960001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.778 Γ— 10⁹⁷(98-digit number)
17787099675487600263…59288114091985920001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2732004

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 0739f8c6dd0d52609db96ea9f5d01c450b6eee64bf4d9f843a51cd20374c519d

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 #2,732,004 on Chainz β†—
Circulating Supply:57,996,819 XPMΒ·at block #6,844,055 Β· updates every 60s
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