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Block #300,432

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/8/2013, 2:21:29 PM Β· Difficulty 9.9923 Β· 6,494,553 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
67df60ce7d6f25e138e4a33c2acdc49b69e1e76cf4823db3e177151658c5c03b
View on Chainz β†—

Height

#300,432

Difficulty

9.992291

Transactions

1

Size

198 B

Version

2

Bits

09fe06ce

Nonce

116,898

Timestamp

12/8/2013, 2:21:29 PM

Confirmations

6,494,553

Merkle Root

fec3a1494504076fdfa308c4df1cb2493e6aae596b5eb53d2df03b25206bda50
Transactions (1)
Coinbasefec3a149450407…f03b25206bda50
1 in β†’ 1 out10.0000 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.

3.577 Γ— 10⁸⁹(90-digit number)
35778241877922672848…61133045735157340880
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
3.577 Γ— 10⁸⁹(90-digit number)
35778241877922672848…61133045735157340879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.577 Γ— 10⁸⁹(90-digit number)
35778241877922672848…61133045735157340881
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
7.155 Γ— 10⁸⁹(90-digit number)
71556483755845345696…22266091470314681759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.155 Γ— 10⁸⁹(90-digit number)
71556483755845345696…22266091470314681761
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
1.431 Γ— 10⁹⁰(91-digit number)
14311296751169069139…44532182940629363519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.431 Γ— 10⁹⁰(91-digit number)
14311296751169069139…44532182940629363521
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
2.862 Γ— 10⁹⁰(91-digit number)
28622593502338138278…89064365881258727039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.862 Γ— 10⁹⁰(91-digit number)
28622593502338138278…89064365881258727041
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
5.724 Γ— 10⁹⁰(91-digit number)
57245187004676276557…78128731762517454079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.724 Γ— 10⁹⁰(91-digit number)
57245187004676276557…78128731762517454081
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 300432

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 67df60ce7d6f25e138e4a33c2acdc49b69e1e76cf4823db3e177151658c5c03b

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 #300,432 on Chainz β†—
Circulating Supply:57,603,921 XPMΒ·at block #6,794,984 Β· updates every 60s
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