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Home/Chain Registry/Block #1,682,110

Block #1,682,110

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 6:56:03 PM Β· Difficulty 10.7184 Β· 5,148,537 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e53e6c725f4e8725ec573e82df6e295d9b34c48ced01f403c2928e9a8d5e2d10
View on Chainz β†—

Difficulty

10.718423

Transactions

1

Size

201 B

Version

2

Bits

0ab7ea94

Nonce

406,507,554

Timestamp

7/20/2016, 6:56:03 PM

Confirmations

5,148,537

Merkle Root

65338d3dd6a388de95714e74fcbdc763ff3f9ef65bf4fe8c6b46630263ef2e94
Transactions (1)
Coinbase65338d3dd6a388…46630263ef2e94
1 in β†’ 1 out8.6900 XPM110 B
AQTTnLtb…SiqWBZdM
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.

2.045 Γ— 10⁹⁢(97-digit number)
20453967345152776129…61628609568741321440
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
2.045 Γ— 10⁹⁢(97-digit number)
20453967345152776129…61628609568741321441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.090 Γ— 10⁹⁢(97-digit number)
40907934690305552259…23257219137482642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.181 Γ— 10⁹⁢(97-digit number)
81815869380611104518…46514438274965285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.636 Γ— 10⁹⁷(98-digit number)
16363173876122220903…93028876549930571521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.272 Γ— 10⁹⁷(98-digit number)
32726347752244441807…86057753099861143041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.545 Γ— 10⁹⁷(98-digit number)
65452695504488883615…72115506199722286081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.309 Γ— 10⁹⁸(99-digit number)
13090539100897776723…44231012399444572161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.618 Γ— 10⁹⁸(99-digit number)
26181078201795553446…88462024798889144321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.236 Γ— 10⁹⁸(99-digit number)
52362156403591106892…76924049597778288641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.047 Γ— 10⁹⁹(100-digit number)
10472431280718221378…53848099195556577281
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 1682110

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 e53e6c725f4e8725ec573e82df6e295d9b34c48ced01f403c2928e9a8d5e2d10

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 #1,682,110 on Chainz β†—
Circulating Supply:57,889,301 XPMΒ·at block #6,830,646 Β· updates every 60s
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