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Block #216,185

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/18/2013, 2:31:25 PM Β· Difficulty 9.9257 Β· 6,610,142 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eeba117bb794b93d3fc1a955c5009dfe4f2e0192d0bfb42c7b841804c93792f9
View on Chainz β†—

Height

#216,185

Difficulty

9.925675

Transactions

1

Size

208 B

Version

2

Bits

09ecf90d

Nonce

16,777,660

Timestamp

10/18/2013, 2:31:25 PM

Confirmations

6,610,142

Merkle Root

253cca0cd4bd135a9d44dc48eb3bbf0623a0af7b1c8f31ca72fd890ea6988074
Transactions (1)
Coinbase253cca0cd4bd13…fd890ea6988074
1 in β†’ 1 out10.1400 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.

5.866 Γ— 10⁹⁸(99-digit number)
58660849636324558639…39211952335914197800
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
5.866 Γ— 10⁹⁸(99-digit number)
58660849636324558639…39211952335914197799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.866 Γ— 10⁹⁸(99-digit number)
58660849636324558639…39211952335914197801
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
1.173 Γ— 10⁹⁹(100-digit number)
11732169927264911727…78423904671828395599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.173 Γ— 10⁹⁹(100-digit number)
11732169927264911727…78423904671828395601
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
2.346 Γ— 10⁹⁹(100-digit number)
23464339854529823455…56847809343656791199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.346 Γ— 10⁹⁹(100-digit number)
23464339854529823455…56847809343656791201
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
4.692 Γ— 10⁹⁹(100-digit number)
46928679709059646911…13695618687313582399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.692 Γ— 10⁹⁹(100-digit number)
46928679709059646911…13695618687313582401
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
9.385 Γ— 10⁹⁹(100-digit number)
93857359418119293823…27391237374627164799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.385 Γ— 10⁹⁹(100-digit number)
93857359418119293823…27391237374627164801
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 216185

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 eeba117bb794b93d3fc1a955c5009dfe4f2e0192d0bfb42c7b841804c93792f9

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 #216,185 on Chainz β†—
Circulating Supply:57,854,756 XPMΒ·at block #6,826,326 Β· updates every 60s
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