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Block #146,407

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2013, 12:01:37 PM Β· Difficulty 9.8475 Β· 6,650,206 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
022460dbc0bbc38d09940abffcc49f6eaa9f64808f5c2f52d7ea80e0572c6cf3
View on Chainz β†—

Height

#146,407

Difficulty

9.847499

Transactions

1

Size

199 B

Version

2

Bits

09d8f5aa

Nonce

169,411

Timestamp

9/2/2013, 12:01:37 PM

Confirmations

6,650,206

Merkle Root

577cd15536903dd30469d17fa45ff0b5263bc108e30184bf58aad62545fb7bac
Transactions (1)
Coinbase577cd15536903d…aad62545fb7bac
1 in β†’ 1 out10.3000 XPM109 B
ALQFWjAm…CoG6fWbs
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.

8.371 Γ— 10⁹³(94-digit number)
83712567795596292349…38302337069654263680
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
8.371 Γ— 10⁹³(94-digit number)
83712567795596292349…38302337069654263679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.371 Γ— 10⁹³(94-digit number)
83712567795596292349…38302337069654263681
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
1.674 Γ— 10⁹⁴(95-digit number)
16742513559119258469…76604674139308527359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.674 Γ— 10⁹⁴(95-digit number)
16742513559119258469…76604674139308527361
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
3.348 Γ— 10⁹⁴(95-digit number)
33485027118238516939…53209348278617054719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.348 Γ— 10⁹⁴(95-digit number)
33485027118238516939…53209348278617054721
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
6.697 Γ— 10⁹⁴(95-digit number)
66970054236477033879…06418696557234109439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.697 Γ— 10⁹⁴(95-digit number)
66970054236477033879…06418696557234109441
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
1.339 Γ— 10⁹⁡(96-digit number)
13394010847295406775…12837393114468218879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 146407

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 022460dbc0bbc38d09940abffcc49f6eaa9f64808f5c2f52d7ea80e0572c6cf3

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 #146,407 on Chainz β†—
Circulating Supply:57,616,901 XPMΒ·at block #6,796,612 Β· updates every 60s
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