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Block #320,633

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2013, 7:07:06 PM Β· Difficulty 10.1837 Β· 6,478,672 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2032bdea8ad9ab5737bd8f6331b882be4bf0edf686c10af42c47b0d485934e05
View on Chainz β†—

Height

#320,633

Difficulty

10.183704

Transactions

1

Size

206 B

Version

2

Bits

0a2f0737

Nonce

12,603

Timestamp

12/19/2013, 7:07:06 PM

Confirmations

6,478,672

Merkle Root

63ef0c0eabbfd47556cf8f11397da1319ebc627492b3fbad0d96eea019a5dcce
Transactions (1)
Coinbase63ef0c0eabbfd4…96eea019a5dcce
1 in β†’ 1 out9.6300 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.

7.691 Γ— 10⁹⁡(96-digit number)
76919783756971112462…88393693572890217440
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
7.691 Γ— 10⁹⁡(96-digit number)
76919783756971112462…88393693572890217439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.691 Γ— 10⁹⁡(96-digit number)
76919783756971112462…88393693572890217441
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
1.538 Γ— 10⁹⁢(97-digit number)
15383956751394222492…76787387145780434879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.538 Γ— 10⁹⁢(97-digit number)
15383956751394222492…76787387145780434881
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
3.076 Γ— 10⁹⁢(97-digit number)
30767913502788444985…53574774291560869759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.076 Γ— 10⁹⁢(97-digit number)
30767913502788444985…53574774291560869761
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
6.153 Γ— 10⁹⁢(97-digit number)
61535827005576889970…07149548583121739519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.153 Γ— 10⁹⁢(97-digit number)
61535827005576889970…07149548583121739521
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
1.230 Γ— 10⁹⁷(98-digit number)
12307165401115377994…14299097166243479039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.230 Γ— 10⁹⁷(98-digit number)
12307165401115377994…14299097166243479041
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 320633

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 2032bdea8ad9ab5737bd8f6331b882be4bf0edf686c10af42c47b0d485934e05

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 #320,633 on Chainz β†—
Circulating Supply:57,638,485 XPMΒ·at block #6,799,304 Β· updates every 60s
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