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Block #454,667

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/22/2014, 2:42:27 AM Β· Difficulty 10.3964 Β· 6,372,039 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dbee9d5055736a605bda385861761c4e2fcd5d080c54dff6e81ecae6c07f78fa
View on Chainz β†—

Height

#454,667

Difficulty

10.396374

Transactions

1

Size

207 B

Version

2

Bits

0a6578cb

Nonce

26,166

Timestamp

3/22/2014, 2:42:27 AM

Confirmations

6,372,039

Merkle Root

2ff842345f348d3e7d023d9617640e6b9cd6b594a3086699f9a57e743ac2ff69
Transactions (1)
Coinbase2ff842345f348d…a57e743ac2ff69
1 in β†’ 1 out9.2400 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.

1.343 Γ— 10⁹⁷(98-digit number)
13437028070444600873…32196852299060189160
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
1.343 Γ— 10⁹⁷(98-digit number)
13437028070444600873…32196852299060189159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.343 Γ— 10⁹⁷(98-digit number)
13437028070444600873…32196852299060189161
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
2.687 Γ— 10⁹⁷(98-digit number)
26874056140889201746…64393704598120378319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.687 Γ— 10⁹⁷(98-digit number)
26874056140889201746…64393704598120378321
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
5.374 Γ— 10⁹⁷(98-digit number)
53748112281778403492…28787409196240756639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.374 Γ— 10⁹⁷(98-digit number)
53748112281778403492…28787409196240756641
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
1.074 Γ— 10⁹⁸(99-digit number)
10749622456355680698…57574818392481513279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.074 Γ— 10⁹⁸(99-digit number)
10749622456355680698…57574818392481513281
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
2.149 Γ— 10⁹⁸(99-digit number)
21499244912711361397…15149636784963026559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.149 Γ— 10⁹⁸(99-digit number)
21499244912711361397…15149636784963026561
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 454667

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 dbee9d5055736a605bda385861761c4e2fcd5d080c54dff6e81ecae6c07f78fa

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 #454,667 on Chainz β†—
Circulating Supply:57,857,800 XPMΒ·at block #6,826,705 Β· updates every 60s
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