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Block #841,383

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/5/2014, 8:30:54 PM Β· Difficulty 10.9740 Β· 5,972,923 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
7e3abb49aa70043ca18da2dfb6fa088b9e7029395488d2acffd1d8c02d606484
View on Chainz β†—

Height

#841,383

Difficulty

10.974033

Transactions

2

Size

433 B

Version

2

Bits

0af95a3c

Nonce

241,758,042

Timestamp

12/5/2014, 8:30:54 PM

Confirmations

5,972,923

Merkle Root

f7626d3031051c788d22c58752144606681716011d6d46226ae0218ba32a94e2
Transactions (2)
Coinbaseba0ce9adfddc3a…bd556426efd57e
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
10200554e0a6c6…e548cc736c0794
1 in β†’ 2 out1.2723 XPM226 B
Acibz2hH…4KK9AWqCARSX6BcD…xndGJQwG
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.

1.059 Γ— 10⁹⁢(97-digit number)
10593935478850921441…76521252460124476800
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.059 Γ— 10⁹⁢(97-digit number)
10593935478850921441…76521252460124476799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.059 Γ— 10⁹⁢(97-digit number)
10593935478850921441…76521252460124476801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.118 Γ— 10⁹⁢(97-digit number)
21187870957701842882…53042504920248953599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.118 Γ— 10⁹⁢(97-digit number)
21187870957701842882…53042504920248953601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.237 Γ— 10⁹⁢(97-digit number)
42375741915403685764…06085009840497907199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.237 Γ— 10⁹⁢(97-digit number)
42375741915403685764…06085009840497907201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
8.475 Γ— 10⁹⁢(97-digit number)
84751483830807371528…12170019680995814399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.475 Γ— 10⁹⁢(97-digit number)
84751483830807371528…12170019680995814401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.695 Γ— 10⁹⁷(98-digit number)
16950296766161474305…24340039361991628799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.695 Γ— 10⁹⁷(98-digit number)
16950296766161474305…24340039361991628801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 841383

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 7e3abb49aa70043ca18da2dfb6fa088b9e7029395488d2acffd1d8c02d606484

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 #841,383 on Chainz β†—
Circulating Supply:57,758,510 XPMΒ·at block #6,814,305 Β· updates every 60s
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