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Block #330,922

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/27/2013, 12:24:24 AM Β· Difficulty 10.1687 Β· 6,495,391 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2655f82be5dc5a5a11933e3de6eac81a28292be8089bc3ac0db79e5660c87574
View on Chainz β†—

Height

#330,922

Difficulty

10.168694

Transactions

1

Size

208 B

Version

2

Bits

0a2b2f82

Nonce

52,604

Timestamp

12/27/2013, 12:24:24 AM

Confirmations

6,495,391

Merkle Root

e262122e62c9fe074524ce99720cc1457c73d79ac0830ed481e7d87a312d94ca
Transactions (1)
Coinbasee262122e62c9fe…e7d87a312d94ca
1 in β†’ 1 out9.6600 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.

4.881 Γ— 10⁹⁹(100-digit number)
48819315717893500511…17966758262036367360
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
4.881 Γ— 10⁹⁹(100-digit number)
48819315717893500511…17966758262036367359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.881 Γ— 10⁹⁹(100-digit number)
48819315717893500511…17966758262036367361
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
9.763 Γ— 10⁹⁹(100-digit number)
97638631435787001022…35933516524072734719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.763 Γ— 10⁹⁹(100-digit number)
97638631435787001022…35933516524072734721
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
1.952 Γ— 10¹⁰⁰(101-digit number)
19527726287157400204…71867033048145469439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.952 Γ— 10¹⁰⁰(101-digit number)
19527726287157400204…71867033048145469441
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
3.905 Γ— 10¹⁰⁰(101-digit number)
39055452574314800409…43734066096290938879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.905 Γ— 10¹⁰⁰(101-digit number)
39055452574314800409…43734066096290938881
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
7.811 Γ— 10¹⁰⁰(101-digit number)
78110905148629600818…87468132192581877759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.811 Γ— 10¹⁰⁰(101-digit number)
78110905148629600818…87468132192581877761
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 330922

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 2655f82be5dc5a5a11933e3de6eac81a28292be8089bc3ac0db79e5660c87574

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 #330,922 on Chainz β†—
Circulating Supply:57,854,642 XPMΒ·at block #6,826,312 Β· updates every 60s
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