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Block #332,709

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/28/2013, 6:29:04 AM Β· Difficulty 10.1667 Β· 6,467,829 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2780b33a32a29c11f26ebc6e8768cc93b4253c67e5fe07449e4e6a280c099089
View on Chainz β†—

Height

#332,709

Difficulty

10.166665

Transactions

1

Size

202 B

Version

2

Bits

0a2aaa87

Nonce

256,602

Timestamp

12/28/2013, 6:29:04 AM

Confirmations

6,467,829

Merkle Root

3a9be1ce173850a09300b8d862f224df86547f0aae804f4dd9dc903917854965
Transactions (1)
Coinbase3a9be1ce173850…dc903917854965
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.

3.190 Γ— 10¹⁰⁰(101-digit number)
31903959376342915841…32303885547101414400
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
3.190 Γ— 10¹⁰⁰(101-digit number)
31903959376342915841…32303885547101414399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.190 Γ— 10¹⁰⁰(101-digit number)
31903959376342915841…32303885547101414401
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
6.380 Γ— 10¹⁰⁰(101-digit number)
63807918752685831683…64607771094202828799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.380 Γ— 10¹⁰⁰(101-digit number)
63807918752685831683…64607771094202828801
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
1.276 Γ— 10¹⁰¹(102-digit number)
12761583750537166336…29215542188405657599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.276 Γ— 10¹⁰¹(102-digit number)
12761583750537166336…29215542188405657601
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
2.552 Γ— 10¹⁰¹(102-digit number)
25523167501074332673…58431084376811315199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.552 Γ— 10¹⁰¹(102-digit number)
25523167501074332673…58431084376811315201
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
5.104 Γ— 10¹⁰¹(102-digit number)
51046335002148665347…16862168753622630399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.104 Γ— 10¹⁰¹(102-digit number)
51046335002148665347…16862168753622630401
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 332709

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 2780b33a32a29c11f26ebc6e8768cc93b4253c67e5fe07449e4e6a280c099089

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 #332,709 on Chainz β†—
Circulating Supply:57,648,366 XPMΒ·at block #6,800,537 Β· updates every 60s
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