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Block #269,810

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/23/2013, 11:37:56 AM Β· Difficulty 9.9522 Β· 6,526,178 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
81a257658e72c640c8339d96c35ad8050e3873c2d5fdbc964f8bd2190ffa38c6
View on Chainz β†—

Height

#269,810

Difficulty

9.952177

Transactions

1

Size

208 B

Version

2

Bits

09f3c1df

Nonce

1,015

Timestamp

11/23/2013, 11:37:56 AM

Confirmations

6,526,178

Merkle Root

cf2208e7b321f96b99993096dbf735511a00fb4c9f6774e200802b4e1d3288f9
Transactions (1)
Coinbasecf2208e7b321f9…802b4e1d3288f9
1 in β†’ 1 out10.0800 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.

2.079 Γ— 10⁹⁹(100-digit number)
20799701065233673210…08520738928613130240
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
2.079 Γ— 10⁹⁹(100-digit number)
20799701065233673210…08520738928613130239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.079 Γ— 10⁹⁹(100-digit number)
20799701065233673210…08520738928613130241
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
4.159 Γ— 10⁹⁹(100-digit number)
41599402130467346420…17041477857226260479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.159 Γ— 10⁹⁹(100-digit number)
41599402130467346420…17041477857226260481
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
8.319 Γ— 10⁹⁹(100-digit number)
83198804260934692841…34082955714452520959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.319 Γ— 10⁹⁹(100-digit number)
83198804260934692841…34082955714452520961
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
1.663 Γ— 10¹⁰⁰(101-digit number)
16639760852186938568…68165911428905041919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.663 Γ— 10¹⁰⁰(101-digit number)
16639760852186938568…68165911428905041921
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
3.327 Γ— 10¹⁰⁰(101-digit number)
33279521704373877136…36331822857810083839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.327 Γ— 10¹⁰⁰(101-digit number)
33279521704373877136…36331822857810083841
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 269810

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 81a257658e72c640c8339d96c35ad8050e3873c2d5fdbc964f8bd2190ffa38c6

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 #269,810 on Chainz β†—
Circulating Supply:57,611,999 XPMΒ·at block #6,795,987 Β· updates every 60s
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