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Block #368,747

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/20/2014, 10:23:38 PM Β· Difficulty 10.4454 Β· 6,433,071 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1d43f9a4f0d7b956c6bd6cbb6ee3a15315efbc7ee202e31b35a5185b75a774f3
View on Chainz β†—

Height

#368,747

Difficulty

10.445423

Transactions

1

Size

208 B

Version

2

Bits

0a720739

Nonce

126,205

Timestamp

1/20/2014, 10:23:38 PM

Confirmations

6,433,071

Merkle Root

7287abcefe00ceec7cdfe813c1d895ed1c6455666ccc474a96b7d5821ab899a2
Transactions (1)
Coinbase7287abcefe00ce…b7d5821ab899a2
1 in β†’ 1 out9.1500 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.

2.315 Γ— 10⁹⁸(99-digit number)
23157466769821385477…58569440761811594240
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
2.315 Γ— 10⁹⁸(99-digit number)
23157466769821385477…58569440761811594239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.315 Γ— 10⁹⁸(99-digit number)
23157466769821385477…58569440761811594241
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
4.631 Γ— 10⁹⁸(99-digit number)
46314933539642770955…17138881523623188479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.631 Γ— 10⁹⁸(99-digit number)
46314933539642770955…17138881523623188481
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
9.262 Γ— 10⁹⁸(99-digit number)
92629867079285541911…34277763047246376959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.262 Γ— 10⁹⁸(99-digit number)
92629867079285541911…34277763047246376961
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
1.852 Γ— 10⁹⁹(100-digit number)
18525973415857108382…68555526094492753919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.852 Γ— 10⁹⁹(100-digit number)
18525973415857108382…68555526094492753921
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
3.705 Γ— 10⁹⁹(100-digit number)
37051946831714216764…37111052188985507839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.705 Γ— 10⁹⁹(100-digit number)
37051946831714216764…37111052188985507841
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 368747

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 1d43f9a4f0d7b956c6bd6cbb6ee3a15315efbc7ee202e31b35a5185b75a774f3

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 #368,747 on Chainz β†—
Circulating Supply:57,658,636 XPMΒ·at block #6,801,817 Β· updates every 60s
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