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Block #297,645

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2013, 5:55:32 PM Β· Difficulty 9.9920 Β· 6,528,911 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
14b068584b470d23aca583dd4d888df9e9041b79ea311e0c33579928cacff909
View on Chainz β†—

Height

#297,645

Difficulty

9.992013

Transactions

1

Size

205 B

Version

2

Bits

09fdf48b

Nonce

89,850

Timestamp

12/6/2013, 5:55:32 PM

Confirmations

6,528,911

Merkle Root

91c95de5e05ae57668c9fd20aafb18610d08c7cf32a28b4ac8eb34e566c4850e
Transactions (1)
Coinbase91c95de5e05ae5…eb34e566c4850e
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.

4.598 Γ— 10⁹¹(92-digit number)
45987195824845916359…89535291758400326720
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
4.598 Γ— 10⁹¹(92-digit number)
45987195824845916359…89535291758400326719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.598 Γ— 10⁹¹(92-digit number)
45987195824845916359…89535291758400326721
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
9.197 Γ— 10⁹¹(92-digit number)
91974391649691832718…79070583516800653439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.197 Γ— 10⁹¹(92-digit number)
91974391649691832718…79070583516800653441
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
1.839 Γ— 10⁹²(93-digit number)
18394878329938366543…58141167033601306879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.839 Γ— 10⁹²(93-digit number)
18394878329938366543…58141167033601306881
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
3.678 Γ— 10⁹²(93-digit number)
36789756659876733087…16282334067202613759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.678 Γ— 10⁹²(93-digit number)
36789756659876733087…16282334067202613761
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
7.357 Γ— 10⁹²(93-digit number)
73579513319753466174…32564668134405227519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.357 Γ— 10⁹²(93-digit number)
73579513319753466174…32564668134405227521
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 297645

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 14b068584b470d23aca583dd4d888df9e9041b79ea311e0c33579928cacff909

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 #297,645 on Chainz β†—
Circulating Supply:57,856,599 XPMΒ·at block #6,826,555 Β· updates every 60s
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