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Block #212,280

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/16/2013, 4:49:06 AM Β· Difficulty 9.9186 Β· 6,612,357 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a2c284fb60ccad28a600012b82fb40ebb84adefedeefeb0169e5b0bac0653da
View on Chainz β†—

Height

#212,280

Difficulty

9.918607

Transactions

1

Size

208 B

Version

2

Bits

09eb29d1

Nonce

562,731

Timestamp

10/16/2013, 4:49:06 AM

Confirmations

6,612,357

Merkle Root

df2a4b467f742a7f956e477f08a4a0f8a4b99e139aa8fc5dead741970c57b9b2
Transactions (1)
Coinbasedf2a4b467f742a…d741970c57b9b2
1 in β†’ 1 out10.1500 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.

4.900 Γ— 10⁹⁸(99-digit number)
49007799954045715402…74472429384286348680
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
4.900 Γ— 10⁹⁸(99-digit number)
49007799954045715402…74472429384286348679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.900 Γ— 10⁹⁸(99-digit number)
49007799954045715402…74472429384286348681
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
9.801 Γ— 10⁹⁸(99-digit number)
98015599908091430805…48944858768572697359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.801 Γ— 10⁹⁸(99-digit number)
98015599908091430805…48944858768572697361
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
1.960 Γ— 10⁹⁹(100-digit number)
19603119981618286161…97889717537145394719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.960 Γ— 10⁹⁹(100-digit number)
19603119981618286161…97889717537145394721
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
3.920 Γ— 10⁹⁹(100-digit number)
39206239963236572322…95779435074290789439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.920 Γ— 10⁹⁹(100-digit number)
39206239963236572322…95779435074290789441
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
7.841 Γ— 10⁹⁹(100-digit number)
78412479926473144644…91558870148581578879
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 212280

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 5a2c284fb60ccad28a600012b82fb40ebb84adefedeefeb0169e5b0bac0653da

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 #212,280 on Chainz β†—
Circulating Supply:57,841,160 XPMΒ·at block #6,824,636 Β· updates every 60s
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