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Block #319,666

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2013, 4:16:33 AM Β· Difficulty 10.1709 Β· 6,477,929 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6913e220287bff875b318cf592c4f57dd50638d2c87c5fc32c217be8f59d757a
View on Chainz β†—

Height

#319,666

Difficulty

10.170881

Transactions

1

Size

203 B

Version

2

Bits

0a2bbed6

Nonce

40,994

Timestamp

12/19/2013, 4:16:33 AM

Confirmations

6,477,929

Merkle Root

9854628cbaf7d987452b9c61b81a89fae3826fa0efade9ed28c736c9a077d780
Transactions (1)
Coinbase9854628cbaf7d9…c736c9a077d780
1 in β†’ 1 out9.6500 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.

7.916 Γ— 10¹⁰¹(102-digit number)
79168862327364119102…37514238326909601280
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
7.916 Γ— 10¹⁰¹(102-digit number)
79168862327364119102…37514238326909601279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.916 Γ— 10¹⁰¹(102-digit number)
79168862327364119102…37514238326909601281
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
1.583 Γ— 10¹⁰²(103-digit number)
15833772465472823820…75028476653819202559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.583 Γ— 10¹⁰²(103-digit number)
15833772465472823820…75028476653819202561
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
3.166 Γ— 10¹⁰²(103-digit number)
31667544930945647640…50056953307638405119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.166 Γ— 10¹⁰²(103-digit number)
31667544930945647640…50056953307638405121
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
6.333 Γ— 10¹⁰²(103-digit number)
63335089861891295281…00113906615276810239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.333 Γ— 10¹⁰²(103-digit number)
63335089861891295281…00113906615276810241
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
1.266 Γ— 10¹⁰³(104-digit number)
12667017972378259056…00227813230553620479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.266 Γ— 10¹⁰³(104-digit number)
12667017972378259056…00227813230553620481
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 319666

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 6913e220287bff875b318cf592c4f57dd50638d2c87c5fc32c217be8f59d757a

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 #319,666 on Chainz β†—
Circulating Supply:57,624,740 XPMΒ·at block #6,797,594 Β· updates every 60s
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