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Block #494,280

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/16/2014, 2:29:57 AM Β· Difficulty 10.7158 Β· 6,323,191 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5d760b33f9c8290d85757ba846824b42e4eafb089829223f6e6a08f21d772458
View on Chainz β†—

Height

#494,280

Difficulty

10.715788

Transactions

1

Size

207 B

Version

2

Bits

0ab73dea

Nonce

262,650,508

Timestamp

4/16/2014, 2:29:57 AM

Confirmations

6,323,191

Merkle Root

f06d0b7635273ed75be52d2e6e7679e5a99fffa6a5037ed16c01d9c44c3047ae
Transactions (1)
Coinbasef06d0b7635273e…01d9c44c3047ae
1 in β†’ 1 out8.6900 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.

2.290 Γ— 10⁹⁷(98-digit number)
22904333149806825874…73704147482550443320
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
2.290 Γ— 10⁹⁷(98-digit number)
22904333149806825874…73704147482550443319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.290 Γ— 10⁹⁷(98-digit number)
22904333149806825874…73704147482550443321
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
4.580 Γ— 10⁹⁷(98-digit number)
45808666299613651748…47408294965100886639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.580 Γ— 10⁹⁷(98-digit number)
45808666299613651748…47408294965100886641
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
9.161 Γ— 10⁹⁷(98-digit number)
91617332599227303496…94816589930201773279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.161 Γ— 10⁹⁷(98-digit number)
91617332599227303496…94816589930201773281
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
1.832 Γ— 10⁹⁸(99-digit number)
18323466519845460699…89633179860403546559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.832 Γ— 10⁹⁸(99-digit number)
18323466519845460699…89633179860403546561
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
3.664 Γ— 10⁹⁸(99-digit number)
36646933039690921398…79266359720807093119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.664 Γ— 10⁹⁸(99-digit number)
36646933039690921398…79266359720807093121
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 494280

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 5d760b33f9c8290d85757ba846824b42e4eafb089829223f6e6a08f21d772458

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 #494,280 on Chainz β†—
Circulating Supply:57,783,820 XPMΒ·at block #6,817,470 Β· updates every 60s
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