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Block #263,164

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/17/2013, 1:44:12 PM Β· Difficulty 9.9668 Β· 6,531,646 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ffe4e6f4c6c4571afdc6a58d26892abab1efb3d2538cbf686029c76ffa64cc59
View on Chainz β†—

Height

#263,164

Difficulty

9.966758

Transactions

1

Size

208 B

Version

2

Bits

09f77d71

Nonce

52,165

Timestamp

11/17/2013, 1:44:12 PM

Confirmations

6,531,646

Merkle Root

979b165fa94f258beb6fc4c058c4964cb0b800d17f5d33e7755a7df09ad69b77
Transactions (1)
Coinbase979b165fa94f25…5a7df09ad69b77
1 in β†’ 1 out10.0500 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.

1.104 Γ— 10¹⁰⁰(101-digit number)
11049194843399948509…19345166399868157260
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
1.104 Γ— 10¹⁰⁰(101-digit number)
11049194843399948509…19345166399868157259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.104 Γ— 10¹⁰⁰(101-digit number)
11049194843399948509…19345166399868157261
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
2.209 Γ— 10¹⁰⁰(101-digit number)
22098389686799897019…38690332799736314519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.209 Γ— 10¹⁰⁰(101-digit number)
22098389686799897019…38690332799736314521
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
4.419 Γ— 10¹⁰⁰(101-digit number)
44196779373599794039…77380665599472629039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.419 Γ— 10¹⁰⁰(101-digit number)
44196779373599794039…77380665599472629041
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
8.839 Γ— 10¹⁰⁰(101-digit number)
88393558747199588079…54761331198945258079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.839 Γ— 10¹⁰⁰(101-digit number)
88393558747199588079…54761331198945258081
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
1.767 Γ— 10¹⁰¹(102-digit number)
17678711749439917615…09522662397890516159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.767 Γ— 10¹⁰¹(102-digit number)
17678711749439917615…09522662397890516161
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 263164

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 ffe4e6f4c6c4571afdc6a58d26892abab1efb3d2538cbf686029c76ffa64cc59

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 #263,164 on Chainz β†—
Circulating Supply:57,602,526 XPMΒ·at block #6,794,809 Β· updates every 60s
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