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Block #296,911

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2013, 7:19:57 AM Β· Difficulty 9.9918 Β· 6,545,546 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
90374b7a747307827108bdb2a350a28c5befa32d0263a5195297e79633b7bc45
View on Chainz β†—

Height

#296,911

Difficulty

9.991832

Transactions

1

Size

205 B

Version

2

Bits

09fde8bc

Nonce

2,325

Timestamp

12/6/2013, 7:19:57 AM

Confirmations

6,545,546

Merkle Root

22e1219b618ff004b5ff4024dd18682d065bc385704ae85b04d4586fba02a936
Transactions (1)
Coinbase22e1219b618ff0…d4586fba02a936
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.

4.328 Γ— 10⁹²(93-digit number)
43287089605111269561…27145066859710888520
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
4.328 Γ— 10⁹²(93-digit number)
43287089605111269561…27145066859710888519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.328 Γ— 10⁹²(93-digit number)
43287089605111269561…27145066859710888521
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
8.657 Γ— 10⁹²(93-digit number)
86574179210222539122…54290133719421777039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.657 Γ— 10⁹²(93-digit number)
86574179210222539122…54290133719421777041
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
1.731 Γ— 10⁹³(94-digit number)
17314835842044507824…08580267438843554079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.731 Γ— 10⁹³(94-digit number)
17314835842044507824…08580267438843554081
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
3.462 Γ— 10⁹³(94-digit number)
34629671684089015648…17160534877687108159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.462 Γ— 10⁹³(94-digit number)
34629671684089015648…17160534877687108161
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
6.925 Γ— 10⁹³(94-digit number)
69259343368178031297…34321069755374216319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.925 Γ— 10⁹³(94-digit number)
69259343368178031297…34321069755374216321
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 296911

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 90374b7a747307827108bdb2a350a28c5befa32d0263a5195297e79633b7bc45

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 #296,911 on Chainz β†—
Circulating Supply:57,984,073 XPMΒ·at block #6,842,456 Β· updates every 60s
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