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Block #492,647

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/15/2014, 6:54:49 AM Β· Difficulty 10.6881 Β· 6,331,846 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7b0b349bae7c277c3aa506dbbc664a1bee7b6227aa8040b06c48d5fadca7adcb
View on Chainz β†—

Height

#492,647

Difficulty

10.688104

Transactions

1

Size

208 B

Version

2

Bits

0ab0278f

Nonce

712,825,405

Timestamp

4/15/2014, 6:54:49 AM

Confirmations

6,331,846

Merkle Root

356ea8d7030e47349d83b6e09359debd78a1354a721623f563a30e49615c62b1
Transactions (1)
Coinbase356ea8d7030e47…a30e49615c62b1
1 in β†’ 1 out8.7400 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.

7.203 Γ— 10⁹⁹(100-digit number)
72036692418070060346…95391778790505625600
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
7.203 Γ— 10⁹⁹(100-digit number)
72036692418070060346…95391778790505625599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.203 Γ— 10⁹⁹(100-digit number)
72036692418070060346…95391778790505625601
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
1.440 Γ— 10¹⁰⁰(101-digit number)
14407338483614012069…90783557581011251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.440 Γ— 10¹⁰⁰(101-digit number)
14407338483614012069…90783557581011251201
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
2.881 Γ— 10¹⁰⁰(101-digit number)
28814676967228024138…81567115162022502399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.881 Γ— 10¹⁰⁰(101-digit number)
28814676967228024138…81567115162022502401
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
5.762 Γ— 10¹⁰⁰(101-digit number)
57629353934456048277…63134230324045004799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.762 Γ— 10¹⁰⁰(101-digit number)
57629353934456048277…63134230324045004801
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
1.152 Γ— 10¹⁰¹(102-digit number)
11525870786891209655…26268460648090009599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.152 Γ— 10¹⁰¹(102-digit number)
11525870786891209655…26268460648090009601
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 492647

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 7b0b349bae7c277c3aa506dbbc664a1bee7b6227aa8040b06c48d5fadca7adcb

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 #492,647 on Chainz β†—
Circulating Supply:57,840,016 XPMΒ·at block #6,824,492 Β· updates every 60s
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