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Block #211,282

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 3:35:08 PM Β· Difficulty 9.9152 Β· 6,583,184 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ead69f39e4ebad9bfa47172f632ea4db5fd71a5abed408998ccc4f9ff244c324
View on Chainz β†—

Height

#211,282

Difficulty

9.915173

Transactions

1

Size

199 B

Version

2

Bits

09ea48c2

Nonce

142,003

Timestamp

10/15/2013, 3:35:08 PM

Confirmations

6,583,184

Merkle Root

0333a81c9a8c28dc2a50313924f7564a3aaa3da75e95df9aa1f4174bda6b652a
Transactions (1)
Coinbase0333a81c9a8c28…f4174bda6b652a
1 in β†’ 1 out10.1600 XPM109 B
AdzHw2Wz…eDZ5XoMj
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.

1.472 Γ— 10⁹⁡(96-digit number)
14723780197085277550…57887733708539487160
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
1.472 Γ— 10⁹⁡(96-digit number)
14723780197085277550…57887733708539487159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.472 Γ— 10⁹⁡(96-digit number)
14723780197085277550…57887733708539487161
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
2.944 Γ— 10⁹⁡(96-digit number)
29447560394170555101…15775467417078974319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.944 Γ— 10⁹⁡(96-digit number)
29447560394170555101…15775467417078974321
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
5.889 Γ— 10⁹⁡(96-digit number)
58895120788341110203…31550934834157948639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.889 Γ— 10⁹⁡(96-digit number)
58895120788341110203…31550934834157948641
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
1.177 Γ— 10⁹⁢(97-digit number)
11779024157668222040…63101869668315897279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.177 Γ— 10⁹⁢(97-digit number)
11779024157668222040…63101869668315897281
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
2.355 Γ— 10⁹⁢(97-digit number)
23558048315336444081…26203739336631794559
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 211282

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 ead69f39e4ebad9bfa47172f632ea4db5fd71a5abed408998ccc4f9ff244c324

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 #211,282 on Chainz β†—
Circulating Supply:57,599,770 XPMΒ·at block #6,794,465 Β· updates every 60s
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