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Block #11,354

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/11/2013, 6:20:41 AM Β· Difficulty 7.7152 Β· 6,794,312 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2a26df58f8d7866e5b3f9b80533625b0e074974c2cbdcacaa405731dccead631
View on Chainz β†—

Height

#11,354

Difficulty

7.715239

Transactions

1

Size

196 B

Version

2

Bits

07b719e9

Nonce

634

Timestamp

7/11/2013, 6:20:41 AM

Confirmations

6,794,312

Merkle Root

af1ef40092fa7038e19dc23b059f7816d3e754900200b317ac902df003aea76f
Transactions (1)
Coinbaseaf1ef40092fa70…902df003aea76f
1 in β†’ 1 out16.7800 XPM108 B
AM6VRLKv…ByN91i1u
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.

1.260 Γ— 10⁹⁰(91-digit number)
12607062984897511678…05916013210981265040
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
1.260 Γ— 10⁹⁰(91-digit number)
12607062984897511678…05916013210981265039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.260 Γ— 10⁹⁰(91-digit number)
12607062984897511678…05916013210981265041
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
2.521 Γ— 10⁹⁰(91-digit number)
25214125969795023356…11832026421962530079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.521 Γ— 10⁹⁰(91-digit number)
25214125969795023356…11832026421962530081
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
5.042 Γ— 10⁹⁰(91-digit number)
50428251939590046712…23664052843925060159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.042 Γ— 10⁹⁰(91-digit number)
50428251939590046712…23664052843925060161
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
1.008 Γ— 10⁹¹(92-digit number)
10085650387918009342…47328105687850120319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 11354

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 2a26df58f8d7866e5b3f9b80533625b0e074974c2cbdcacaa405731dccead631

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 #11,354 on Chainz β†—
Circulating Supply:57,689,406 XPMΒ·at block #6,805,665 Β· updates every 60s
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