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Block #321,364

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/20/2013, 6:42:45 AM Β· Difficulty 10.1899 Β· 6,480,649 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8c59153e4de31963108a5c0434c488757b3c6f88f7c0de749903db581b51bc72
View on Chainz β†—

Height

#321,364

Difficulty

10.189889

Transactions

1

Size

211 B

Version

2

Bits

0a309c8c

Nonce

1,600

Timestamp

12/20/2013, 6:42:45 AM

Confirmations

6,480,649

Merkle Root

cf263f49e6f411d6b542b7375efca5c78184b9c28d64b0c29d8acda5d54890b0
Transactions (1)
Coinbasecf263f49e6f411…8acda5d54890b0
1 in β†’ 1 out9.6200 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.

1.590 Γ— 10¹⁰⁢(107-digit number)
15902437346547695955…12780861279657000960
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
1.590 Γ— 10¹⁰⁢(107-digit number)
15902437346547695955…12780861279657000959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.590 Γ— 10¹⁰⁢(107-digit number)
15902437346547695955…12780861279657000961
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
3.180 Γ— 10¹⁰⁢(107-digit number)
31804874693095391910…25561722559314001919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.180 Γ— 10¹⁰⁢(107-digit number)
31804874693095391910…25561722559314001921
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
6.360 Γ— 10¹⁰⁢(107-digit number)
63609749386190783821…51123445118628003839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.360 Γ— 10¹⁰⁢(107-digit number)
63609749386190783821…51123445118628003841
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
1.272 Γ— 10¹⁰⁷(108-digit number)
12721949877238156764…02246890237256007679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.272 Γ— 10¹⁰⁷(108-digit number)
12721949877238156764…02246890237256007681
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
2.544 Γ— 10¹⁰⁷(108-digit number)
25443899754476313528…04493780474512015359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.544 Γ— 10¹⁰⁷(108-digit number)
25443899754476313528…04493780474512015361
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 321364

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 8c59153e4de31963108a5c0434c488757b3c6f88f7c0de749903db581b51bc72

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 #321,364 on Chainz β†—
Circulating Supply:57,660,194 XPMΒ·at block #6,802,012 Β· updates every 60s
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