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Block #393,003

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/6/2014, 7:55:00 PM Β· Difficulty 10.4441 Β· 6,423,019 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f391537e7a2a11dbc71db8e8075ecf92ebb4bdb6a437019749fb17cd3840fde2
View on Chainz β†—

Height

#393,003

Difficulty

10.444055

Transactions

1

Size

207 B

Version

2

Bits

0a71ad95

Nonce

2,800

Timestamp

2/6/2014, 7:55:00 PM

Confirmations

6,423,019

Merkle Root

9ac4df317f3e3abd31c4ac664718037c87c476b8a37fcbf85ffe4624f5a56fc9
Transactions (1)
Coinbase9ac4df317f3e3a…fe4624f5a56fc9
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.

1.541 Γ— 10⁹⁷(98-digit number)
15412974617121004759…47288981231051742990
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
1.541 Γ— 10⁹⁷(98-digit number)
15412974617121004759…47288981231051742989
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.541 Γ— 10⁹⁷(98-digit number)
15412974617121004759…47288981231051742991
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
3.082 Γ— 10⁹⁷(98-digit number)
30825949234242009518…94577962462103485979
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.082 Γ— 10⁹⁷(98-digit number)
30825949234242009518…94577962462103485981
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
6.165 Γ— 10⁹⁷(98-digit number)
61651898468484019036…89155924924206971959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.165 Γ— 10⁹⁷(98-digit number)
61651898468484019036…89155924924206971961
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
1.233 Γ— 10⁹⁸(99-digit number)
12330379693696803807…78311849848413943919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.233 Γ— 10⁹⁸(99-digit number)
12330379693696803807…78311849848413943921
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
2.466 Γ— 10⁹⁸(99-digit number)
24660759387393607614…56623699696827887839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.466 Γ— 10⁹⁸(99-digit number)
24660759387393607614…56623699696827887841
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 393003

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 f391537e7a2a11dbc71db8e8075ecf92ebb4bdb6a437019749fb17cd3840fde2

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 #393,003 on Chainz β†—
Circulating Supply:57,772,288 XPMΒ·at block #6,816,021 Β· updates every 60s
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