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Block #278,818

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2013, 3:18:57 AM Β· Difficulty 9.9700 Β· 6,553,005 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1f64837205dd3da7be2322d7660b4200fc326aed1e10d4649e88062520c5c65a
View on Chainz β†—

Height

#278,818

Difficulty

9.969968

Transactions

1

Size

206 B

Version

2

Bits

09f84fd1

Nonce

67,110,253

Timestamp

11/28/2013, 3:18:57 AM

Confirmations

6,553,005

Merkle Root

b812fd364888ba94134ce55f241d1f9dbad12fdf9d753acf9191fb20c05098d2
Transactions (1)
Coinbaseb812fd364888ba…91fb20c05098d2
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.

1.186 Γ— 10⁹⁴(95-digit number)
11865725072270961276…62151494655070097620
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
1.186 Γ— 10⁹⁴(95-digit number)
11865725072270961276…62151494655070097619
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.186 Γ— 10⁹⁴(95-digit number)
11865725072270961276…62151494655070097621
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
2.373 Γ— 10⁹⁴(95-digit number)
23731450144541922552…24302989310140195239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.373 Γ— 10⁹⁴(95-digit number)
23731450144541922552…24302989310140195241
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
4.746 Γ— 10⁹⁴(95-digit number)
47462900289083845105…48605978620280390479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.746 Γ— 10⁹⁴(95-digit number)
47462900289083845105…48605978620280390481
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
9.492 Γ— 10⁹⁴(95-digit number)
94925800578167690210…97211957240560780959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.492 Γ— 10⁹⁴(95-digit number)
94925800578167690210…97211957240560780961
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
1.898 Γ— 10⁹⁡(96-digit number)
18985160115633538042…94423914481121561919
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 278818

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 1f64837205dd3da7be2322d7660b4200fc326aed1e10d4649e88062520c5c65a

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 #278,818 on Chainz β†—
Circulating Supply:57,898,701 XPMΒ·at block #6,831,822 Β· updates every 60s
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