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Block #296,830

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2013, 6:07:19 AM Β· Difficulty 9.9918 Β· 6,548,431 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
663f28f461276cf4331092d6fa367c38f2a90a96b9aaed25fda922201de22a97
View on Chainz β†—

Height

#296,830

Difficulty

9.991816

Transactions

1

Size

206 B

Version

2

Bits

09fde7a9

Nonce

225,718

Timestamp

12/6/2013, 6:07:19 AM

Confirmations

6,548,431

Merkle Root

b8d3447ba24473be151ad23bb0882530e6dea15a762955d0ec8a6ead08755a08
Transactions (1)
Coinbaseb8d3447ba24473…8a6ead08755a08
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

9.792 Γ— 10⁹⁴(95-digit number)
97921080754736765879…15665766439340160000
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
9.792 Γ— 10⁹⁴(95-digit number)
97921080754736765879…15665766439340159999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.792 Γ— 10⁹⁴(95-digit number)
97921080754736765879…15665766439340160001
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
1.958 Γ— 10⁹⁡(96-digit number)
19584216150947353175…31331532878680319999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.958 Γ— 10⁹⁡(96-digit number)
19584216150947353175…31331532878680320001
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
3.916 Γ— 10⁹⁡(96-digit number)
39168432301894706351…62663065757360639999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.916 Γ— 10⁹⁡(96-digit number)
39168432301894706351…62663065757360640001
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
7.833 Γ— 10⁹⁡(96-digit number)
78336864603789412703…25326131514721279999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.833 Γ— 10⁹⁡(96-digit number)
78336864603789412703…25326131514721280001
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
1.566 Γ— 10⁹⁢(97-digit number)
15667372920757882540…50652263029442559999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.566 Γ— 10⁹⁢(97-digit number)
15667372920757882540…50652263029442560001
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 296830

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 663f28f461276cf4331092d6fa367c38f2a90a96b9aaed25fda922201de22a97

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 #296,830 on Chainz β†—
Circulating Supply:58,006,522 XPMΒ·at block #6,845,260 Β· updates every 60s
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