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Block #333,004

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/28/2013, 11:28:58 AM Β· Difficulty 10.1659 Β· 6,471,990 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4e5fc5d09ed2c3f9caaea968aa07f8d498f444da61087281127324efd7f3558f
View on Chainz β†—

Height

#333,004

Difficulty

10.165929

Transactions

1

Size

207 B

Version

2

Bits

0a2a7a54

Nonce

865,326

Timestamp

12/28/2013, 11:28:58 AM

Confirmations

6,471,990

Merkle Root

5991e2cdd4e1fd8aad0f2eee834cafc4393fa745a6ea61b51a88025eaaab4978
Transactions (1)
Coinbase5991e2cdd4e1fd…88025eaaab4978
1 in β†’ 1 out9.6600 XPM116 B
AbwWkWZt…kawDhufa
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.

1.882 Γ— 10⁹⁸(99-digit number)
18822774683748387914…91454408172365216320
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
1.882 Γ— 10⁹⁸(99-digit number)
18822774683748387914…91454408172365216319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.882 Γ— 10⁹⁸(99-digit number)
18822774683748387914…91454408172365216321
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
3.764 Γ— 10⁹⁸(99-digit number)
37645549367496775829…82908816344730432639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.764 Γ— 10⁹⁸(99-digit number)
37645549367496775829…82908816344730432641
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
7.529 Γ— 10⁹⁸(99-digit number)
75291098734993551659…65817632689460865279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.529 Γ— 10⁹⁸(99-digit number)
75291098734993551659…65817632689460865281
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
1.505 Γ— 10⁹⁹(100-digit number)
15058219746998710331…31635265378921730559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.505 Γ— 10⁹⁹(100-digit number)
15058219746998710331…31635265378921730561
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
3.011 Γ— 10⁹⁹(100-digit number)
30116439493997420663…63270530757843461119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.011 Γ— 10⁹⁹(100-digit number)
30116439493997420663…63270530757843461121
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 333004

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 4e5fc5d09ed2c3f9caaea968aa07f8d498f444da61087281127324efd7f3558f

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 #333,004 on Chainz β†—
Circulating Supply:57,684,022 XPMΒ·at block #6,804,993 Β· updates every 60s
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