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Block #491,442

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/14/2014, 12:44:00 PM Β· Difficulty 10.6809 Β· 6,335,483 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
50a67d512b52ba01ab4d67c3c75a233d8ebb142bd62cb2dcd65b8b0cc3395fb6
View on Chainz β†—

Height

#491,442

Difficulty

10.680866

Transactions

1

Size

207 B

Version

2

Bits

0aae4d3e

Nonce

179,341,793

Timestamp

4/14/2014, 12:44:00 PM

Confirmations

6,335,483

Merkle Root

1e1551fb65a0362b0f8a2e63a35383a5c12f712477b226f0dcf5f252d91caec1
Transactions (1)
Coinbase1e1551fb65a036…f5f252d91caec1
1 in β†’ 1 out8.7500 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.

6.798 Γ— 10⁹⁷(98-digit number)
67985496536696769133…73614039867148186560
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
6.798 Γ— 10⁹⁷(98-digit number)
67985496536696769133…73614039867148186559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.798 Γ— 10⁹⁷(98-digit number)
67985496536696769133…73614039867148186561
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
1.359 Γ— 10⁹⁸(99-digit number)
13597099307339353826…47228079734296373119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.359 Γ— 10⁹⁸(99-digit number)
13597099307339353826…47228079734296373121
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
2.719 Γ— 10⁹⁸(99-digit number)
27194198614678707653…94456159468592746239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.719 Γ— 10⁹⁸(99-digit number)
27194198614678707653…94456159468592746241
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
5.438 Γ— 10⁹⁸(99-digit number)
54388397229357415306…88912318937185492479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.438 Γ— 10⁹⁸(99-digit number)
54388397229357415306…88912318937185492481
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
1.087 Γ— 10⁹⁹(100-digit number)
10877679445871483061…77824637874370984959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.087 Γ— 10⁹⁹(100-digit number)
10877679445871483061…77824637874370984961
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 491442

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 50a67d512b52ba01ab4d67c3c75a233d8ebb142bd62cb2dcd65b8b0cc3395fb6

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 #491,442 on Chainz β†—
Circulating Supply:57,859,571 XPMΒ·at block #6,826,924 Β· updates every 60s
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