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Home/Chain Registry/Block #2,730,130

Block #2,730,130

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/1/2018, 9:30:51 PM Β· Difficulty 11.6297 Β· 4,115,027 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b29f8835370ecddf1fbb8825717ea6dd309579331a9b467b2ad871dfe94b3c7d
View on Chainz β†—

Difficulty

11.629711

Transactions

1

Size

201 B

Version

2

Bits

0ba134bc

Nonce

1,747,744,190

Timestamp

7/1/2018, 9:30:51 PM

Confirmations

4,115,027

Merkle Root

8b2bb2f55dab560091d676c1ec9b2136feef7c2c04fda6e16a297996d63045f0
Transactions (1)
Coinbase8b2bb2f55dab56…297996d63045f0
1 in β†’ 1 out7.3800 XPM110 B
APPGjA2i…YdwWzgyV
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.

3.548 Γ— 10⁹⁷(98-digit number)
35484234016132098498…58297344821690675200
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
3.548 Γ— 10⁹⁷(98-digit number)
35484234016132098498…58297344821690675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.096 Γ— 10⁹⁷(98-digit number)
70968468032264196997…16594689643381350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.419 Γ— 10⁹⁸(99-digit number)
14193693606452839399…33189379286762700801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.838 Γ— 10⁹⁸(99-digit number)
28387387212905678799…66378758573525401601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.677 Γ— 10⁹⁸(99-digit number)
56774774425811357598…32757517147050803201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.135 Γ— 10⁹⁹(100-digit number)
11354954885162271519…65515034294101606401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.270 Γ— 10⁹⁹(100-digit number)
22709909770324543039…31030068588203212801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.541 Γ— 10⁹⁹(100-digit number)
45419819540649086078…62060137176406425601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.083 Γ— 10⁹⁹(100-digit number)
90839639081298172157…24120274352812851201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.816 Γ— 10¹⁰⁰(101-digit number)
18167927816259634431…48240548705625702401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.633 Γ— 10¹⁰⁰(101-digit number)
36335855632519268862…96481097411251404801
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 2730130

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 b29f8835370ecddf1fbb8825717ea6dd309579331a9b467b2ad871dfe94b3c7d

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 #2,730,130 on Chainz β†—
Circulating Supply:58,005,684 XPMΒ·at block #6,845,156 Β· updates every 60s
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