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Block #330,151

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/26/2013, 11:32:14 AM Β· Difficulty 10.1687 Β· 6,465,758 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4d3f2a7d909f0c77268838cefbe33cd5801251a986fe896563e885bb9d3a7b5
View on Chainz β†—

Height

#330,151

Difficulty

10.168735

Transactions

1

Size

202 B

Version

2

Bits

0a2b323c

Nonce

16,513

Timestamp

12/26/2013, 11:32:14 AM

Confirmations

6,465,758

Merkle Root

aece5acee23366b4153f2c2870e4566a5de5faee84e9818f01ee1f92d0996773
Transactions (1)
Coinbaseaece5acee23366…ee1f92d0996773
1 in β†’ 1 out9.6600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.687 Γ— 10¹⁰⁰(101-digit number)
26870366908742387824…61244176862797381920
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
2.687 Γ— 10¹⁰⁰(101-digit number)
26870366908742387824…61244176862797381919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.687 Γ— 10¹⁰⁰(101-digit number)
26870366908742387824…61244176862797381921
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
5.374 Γ— 10¹⁰⁰(101-digit number)
53740733817484775649…22488353725594763839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.374 Γ— 10¹⁰⁰(101-digit number)
53740733817484775649…22488353725594763841
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
1.074 Γ— 10¹⁰¹(102-digit number)
10748146763496955129…44976707451189527679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.074 Γ— 10¹⁰¹(102-digit number)
10748146763496955129…44976707451189527681
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
2.149 Γ— 10¹⁰¹(102-digit number)
21496293526993910259…89953414902379055359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.149 Γ— 10¹⁰¹(102-digit number)
21496293526993910259…89953414902379055361
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
4.299 Γ— 10¹⁰¹(102-digit number)
42992587053987820519…79906829804758110719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.299 Γ— 10¹⁰¹(102-digit number)
42992587053987820519…79906829804758110721
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 330151

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 b4d3f2a7d909f0c77268838cefbe33cd5801251a986fe896563e885bb9d3a7b5

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 #330,151 on Chainz β†—
Circulating Supply:57,611,357 XPMΒ·at block #6,795,908 Β· updates every 60s
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