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Home/Chain Registry/Block #1,534,742

Block #1,534,742

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 10:53:11 AM Β· Difficulty 10.6180 Β· 5,281,663 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8ed32ee87c014dc229b84754c14cfc07ac35d3f0a4e94fef97189ec568ba2ba0
View on Chainz β†—

Difficulty

10.617990

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e3491

Nonce

248,850,300

Timestamp

4/10/2016, 10:53:11 AM

Confirmations

5,281,663

Merkle Root

e71fcdcc5c86fc475c063cb6cdf611a2a2ed28654b66998c970a36bb7c09b62c
Transactions (2)
Coinbase0583e1421bb3e6…33cc44122ae5b5
1 in β†’ 1 out8.9400 XPM110 B
AN5jE5fY…CgQymPx9
1fd474c7e59ea8…2ceb1d706711f7
51 in β†’ 1 out240.3891 XPM7.41 KB
AHRYQQXR…sEHXnS2k
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.

3.920 Γ— 10⁹²(93-digit number)
39209210135315875837…91149258655166746240
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
3.920 Γ— 10⁹²(93-digit number)
39209210135315875837…91149258655166746241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.841 Γ— 10⁹²(93-digit number)
78418420270631751675…82298517310333492481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.568 Γ— 10⁹³(94-digit number)
15683684054126350335…64597034620666984961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.136 Γ— 10⁹³(94-digit number)
31367368108252700670…29194069241333969921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.273 Γ— 10⁹³(94-digit number)
62734736216505401340…58388138482667939841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.254 Γ— 10⁹⁴(95-digit number)
12546947243301080268…16776276965335879681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.509 Γ— 10⁹⁴(95-digit number)
25093894486602160536…33552553930671759361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.018 Γ— 10⁹⁴(95-digit number)
50187788973204321072…67105107861343518721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.003 Γ— 10⁹⁡(96-digit number)
10037557794640864214…34210215722687037441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.007 Γ— 10⁹⁡(96-digit number)
20075115589281728428…68420431445374074881
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 1534742

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 8ed32ee87c014dc229b84754c14cfc07ac35d3f0a4e94fef97189ec568ba2ba0

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 #1,534,742 on Chainz β†—
Circulating Supply:57,775,365 XPMΒ·at block #6,816,404 Β· updates every 60s
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