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Home/Chain Registry/Block #2,730,141

Block #2,730,141

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/1/2018, 9:41:01 PM Β· Difficulty 11.6298 Β· 4,113,130 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a62e9b07332a12f36278faea8b9042a0ecdb0e0fdf56f30654b2f7c09e254ef0
View on Chainz β†—

Difficulty

11.629804

Transactions

1

Size

200 B

Version

2

Bits

0ba13adc

Nonce

809,887,761

Timestamp

7/1/2018, 9:41:01 PM

Confirmations

4,113,130

Merkle Root

bb1d717db05de72bac3414b3f3aa3c415eb8eed756a11978a3e24c26400f464c
Transactions (1)
Coinbasebb1d717db05de7…e24c26400f464c
1 in β†’ 1 out7.3800 XPM110 B
AKmCqVya…9DKan613
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.

5.534 Γ— 10⁹⁴(95-digit number)
55346053615123128039…71696347886193088000
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
5.534 Γ— 10⁹⁴(95-digit number)
55346053615123128039…71696347886193088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.106 Γ— 10⁹⁡(96-digit number)
11069210723024625607…43392695772386176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.213 Γ— 10⁹⁡(96-digit number)
22138421446049251215…86785391544772352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.427 Γ— 10⁹⁡(96-digit number)
44276842892098502431…73570783089544704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.855 Γ— 10⁹⁡(96-digit number)
88553685784197004863…47141566179089408001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.771 Γ— 10⁹⁢(97-digit number)
17710737156839400972…94283132358178816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.542 Γ— 10⁹⁢(97-digit number)
35421474313678801945…88566264716357632001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.084 Γ— 10⁹⁢(97-digit number)
70842948627357603890…77132529432715264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.416 Γ— 10⁹⁷(98-digit number)
14168589725471520778…54265058865430528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.833 Γ— 10⁹⁷(98-digit number)
28337179450943041556…08530117730861056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.667 Γ— 10⁹⁷(98-digit number)
56674358901886083112…17060235461722112001
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 2730141

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 a62e9b07332a12f36278faea8b9042a0ecdb0e0fdf56f30654b2f7c09e254ef0

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 #2,730,141 on Chainz β†—
Circulating Supply:57,990,542 XPMΒ·at block #6,843,270 Β· updates every 60s
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