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Block #320,279

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2013, 1:17:06 PM Β· Difficulty 10.1828 Β· 6,485,297 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c0d6d217066ddd77c56e9c71f3d140ae1815cae0f3e77aff53db887a2de39e20
View on Chainz β†—

Height

#320,279

Difficulty

10.182772

Transactions

1

Size

208 B

Version

2

Bits

0a2eca2a

Nonce

236,389

Timestamp

12/19/2013, 1:17:06 PM

Confirmations

6,485,297

Merkle Root

b4cfb3b3caf5d068cf7a490e2ca002a9385af04e4db4fb3d4d1d17a11fe240ec
Transactions (1)
Coinbaseb4cfb3b3caf5d0…1d17a11fe240ec
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.

3.368 Γ— 10⁹⁹(100-digit number)
33687650390071487893…65803225070508062400
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
3.368 Γ— 10⁹⁹(100-digit number)
33687650390071487893…65803225070508062399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.368 Γ— 10⁹⁹(100-digit number)
33687650390071487893…65803225070508062401
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
6.737 Γ— 10⁹⁹(100-digit number)
67375300780142975787…31606450141016124799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.737 Γ— 10⁹⁹(100-digit number)
67375300780142975787…31606450141016124801
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
1.347 Γ— 10¹⁰⁰(101-digit number)
13475060156028595157…63212900282032249599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.347 Γ— 10¹⁰⁰(101-digit number)
13475060156028595157…63212900282032249601
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
2.695 Γ— 10¹⁰⁰(101-digit number)
26950120312057190315…26425800564064499199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.695 Γ— 10¹⁰⁰(101-digit number)
26950120312057190315…26425800564064499201
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
5.390 Γ— 10¹⁰⁰(101-digit number)
53900240624114380630…52851601128128998399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.390 Γ— 10¹⁰⁰(101-digit number)
53900240624114380630…52851601128128998401
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 320279

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 c0d6d217066ddd77c56e9c71f3d140ae1815cae0f3e77aff53db887a2de39e20

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 #320,279 on Chainz β†—
Circulating Supply:57,688,684 XPMΒ·at block #6,805,575 Β· updates every 60s
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