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Home/Chain Registry/Block #1,681,643

Block #1,681,643

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 11:43:05 AM Β· Difficulty 10.7165 Β· 5,162,042 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b8b47340fc811ce705f1f90600d720be125a776d8a47e11d380e3a0dd7672b5c
View on Chainz β†—

Difficulty

10.716455

Transactions

1

Size

201 B

Version

2

Bits

0ab7699e

Nonce

579,866,653

Timestamp

7/20/2016, 11:43:05 AM

Confirmations

5,162,042

Merkle Root

44ee5fda576917fc76875f7212b7a9df4617f0b95c9d3208b523edd7a64e9306
Transactions (1)
Coinbase44ee5fda576917…23edd7a64e9306
1 in β†’ 1 out8.6900 XPM110 B
AGBmz1S6…cBwxQ3hc
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.

1.506 Γ— 10⁹⁢(97-digit number)
15067144120600898107…71809314709990876160
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
1.506 Γ— 10⁹⁢(97-digit number)
15067144120600898107…71809314709990876161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.013 Γ— 10⁹⁢(97-digit number)
30134288241201796215…43618629419981752321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.026 Γ— 10⁹⁢(97-digit number)
60268576482403592431…87237258839963504641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.205 Γ— 10⁹⁷(98-digit number)
12053715296480718486…74474517679927009281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.410 Γ— 10⁹⁷(98-digit number)
24107430592961436972…48949035359854018561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.821 Γ— 10⁹⁷(98-digit number)
48214861185922873945…97898070719708037121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.642 Γ— 10⁹⁷(98-digit number)
96429722371845747890…95796141439416074241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.928 Γ— 10⁹⁸(99-digit number)
19285944474369149578…91592282878832148481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.857 Γ— 10⁹⁸(99-digit number)
38571888948738299156…83184565757664296961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.714 Γ— 10⁹⁸(99-digit number)
77143777897476598312…66369131515328593921
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 1681643

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 b8b47340fc811ce705f1f90600d720be125a776d8a47e11d380e3a0dd7672b5c

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 #1,681,643 on Chainz β†—
Circulating Supply:57,993,850 XPMΒ·at block #6,843,684 Β· updates every 60s
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