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Block #258,743

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/13/2013, 5:53:56 AM Β· Difficulty 9.9767 Β· 6,567,733 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8b3f0ad6d20401a82289aab2ba39f8f3d7acd0606576a0c1faad61574086ec92
View on Chainz β†—

Height

#258,743

Difficulty

9.976653

Transactions

1

Size

198 B

Version

2

Bits

09fa05f0

Nonce

62,451

Timestamp

11/13/2013, 5:53:56 AM

Confirmations

6,567,733

Merkle Root

48bf698e26b1f55b617e953861c448fa6b59c3b793f89f49323c3830fc23ca1b
Transactions (1)
Coinbase48bf698e26b1f5…3c3830fc23ca1b
1 in β†’ 1 out10.0300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

9.099 Γ— 10⁸⁸(89-digit number)
90999184926351357269…85602072091033744150
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
9.099 Γ— 10⁸⁸(89-digit number)
90999184926351357269…85602072091033744149
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.099 Γ— 10⁸⁸(89-digit number)
90999184926351357269…85602072091033744151
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
1.819 Γ— 10⁸⁹(90-digit number)
18199836985270271453…71204144182067488299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.819 Γ— 10⁸⁹(90-digit number)
18199836985270271453…71204144182067488301
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
3.639 Γ— 10⁸⁹(90-digit number)
36399673970540542907…42408288364134976599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.639 Γ— 10⁸⁹(90-digit number)
36399673970540542907…42408288364134976601
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
7.279 Γ— 10⁸⁹(90-digit number)
72799347941081085815…84816576728269953199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.279 Γ— 10⁸⁹(90-digit number)
72799347941081085815…84816576728269953201
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
1.455 Γ— 10⁹⁰(91-digit number)
14559869588216217163…69633153456539906399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.455 Γ— 10⁹⁰(91-digit number)
14559869588216217163…69633153456539906401
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 258743

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 8b3f0ad6d20401a82289aab2ba39f8f3d7acd0606576a0c1faad61574086ec92

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 #258,743 on Chainz β†—
Circulating Supply:57,855,946 XPMΒ·at block #6,826,475 Β· updates every 60s
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