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Home/Chain Registry/Block #1,730,897

Block #1,730,897

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/23/2016, 5:26:14 PM Β· Difficulty 10.7153 Β· 5,096,343 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7978e7ea3d008506b9840f7380f11bbb7eea5be13b28ab8e0fc82a6366c7ffed
View on Chainz β†—

Difficulty

10.715333

Transactions

1

Size

199 B

Version

2

Bits

0ab7200b

Nonce

35,171,914

Timestamp

8/23/2016, 5:26:14 PM

Confirmations

5,096,343

Merkle Root

448bcb3de64309f7c49439d6096b8b759c10d94e86f5fd56cdc5f684578d4816
Transactions (1)
Coinbase448bcb3de64309…c5f684578d4816
1 in β†’ 1 out8.7000 XPM109 B
AYaBzo1h…TfpGvFys
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.

4.568 Γ— 10⁹⁡(96-digit number)
45684811964044087772…86781006039111248000
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
4.568 Γ— 10⁹⁡(96-digit number)
45684811964044087772…86781006039111248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.136 Γ— 10⁹⁡(96-digit number)
91369623928088175545…73562012078222496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.827 Γ— 10⁹⁢(97-digit number)
18273924785617635109…47124024156444992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.654 Γ— 10⁹⁢(97-digit number)
36547849571235270218…94248048312889984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.309 Γ— 10⁹⁢(97-digit number)
73095699142470540436…88496096625779968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.461 Γ— 10⁹⁷(98-digit number)
14619139828494108087…76992193251559936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.923 Γ— 10⁹⁷(98-digit number)
29238279656988216174…53984386503119872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.847 Γ— 10⁹⁷(98-digit number)
58476559313976432349…07968773006239744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.169 Γ— 10⁹⁸(99-digit number)
11695311862795286469…15937546012479488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.339 Γ— 10⁹⁸(99-digit number)
23390623725590572939…31875092024958976001
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 1730897

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 7978e7ea3d008506b9840f7380f11bbb7eea5be13b28ab8e0fc82a6366c7ffed

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 #1,730,897 on Chainz β†—
Circulating Supply:57,862,021 XPMΒ·at block #6,827,239 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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