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Block #275,770

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/26/2013, 8:54:40 PM Β· Difficulty 9.9616 Β· 6,550,399 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4f97cd5aac52170a347ad52286ee9f9d36a021d0d064444f70a66735d1a32123
View on Chainz β†—

Height

#275,770

Difficulty

9.961587

Transactions

1

Size

207 B

Version

2

Bits

09f62a8a

Nonce

63,273

Timestamp

11/26/2013, 8:54:40 PM

Confirmations

6,550,399

Merkle Root

623ff27e4655679ea86fe91950d42dcad1d330398134999895fd2bb7ef92ae7c
Transactions (1)
Coinbase623ff27e465567…fd2bb7ef92ae7c
1 in β†’ 1 out10.0600 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.

1.848 Γ— 10⁹⁢(97-digit number)
18485998045098814885…72962818926996044080
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
1.848 Γ— 10⁹⁢(97-digit number)
18485998045098814885…72962818926996044079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.848 Γ— 10⁹⁢(97-digit number)
18485998045098814885…72962818926996044081
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
3.697 Γ— 10⁹⁢(97-digit number)
36971996090197629771…45925637853992088159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.697 Γ— 10⁹⁢(97-digit number)
36971996090197629771…45925637853992088161
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
7.394 Γ— 10⁹⁢(97-digit number)
73943992180395259542…91851275707984176319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.394 Γ— 10⁹⁢(97-digit number)
73943992180395259542…91851275707984176321
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
1.478 Γ— 10⁹⁷(98-digit number)
14788798436079051908…83702551415968352639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.478 Γ— 10⁹⁷(98-digit number)
14788798436079051908…83702551415968352641
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
2.957 Γ— 10⁹⁷(98-digit number)
29577596872158103817…67405102831936705279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 275770

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 4f97cd5aac52170a347ad52286ee9f9d36a021d0d064444f70a66735d1a32123

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 #275,770 on Chainz β†—
Circulating Supply:57,853,480 XPMΒ·at block #6,826,168 Β· updates every 60s
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