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Block #186,199

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2013, 6:48:15 PM Β· Difficulty 9.8646 Β· 6,613,784 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
da7cddff5880bb600e233fb77ba7e3fb9769d2507cf96d41d8d467c2f6664238
View on Chainz β†—

Height

#186,199

Difficulty

9.864611

Transactions

1

Size

208 B

Version

2

Bits

09dd5724

Nonce

563,563

Timestamp

9/29/2013, 6:48:15 PM

Confirmations

6,613,784

Merkle Root

11cd0280a9f0643870636d50c38ccea975a6440bad38bc82bb17a0af660a55b5
Transactions (1)
Coinbase11cd0280a9f064…17a0af660a55b5
1 in β†’ 1 out10.2600 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.

2.523 Γ— 10⁹⁸(99-digit number)
25238040391622340780…73977846757781173650
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
2.523 Γ— 10⁹⁸(99-digit number)
25238040391622340780…73977846757781173649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.523 Γ— 10⁹⁸(99-digit number)
25238040391622340780…73977846757781173651
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
5.047 Γ— 10⁹⁸(99-digit number)
50476080783244681560…47955693515562347299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.047 Γ— 10⁹⁸(99-digit number)
50476080783244681560…47955693515562347301
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
1.009 Γ— 10⁹⁹(100-digit number)
10095216156648936312…95911387031124694599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.009 Γ— 10⁹⁹(100-digit number)
10095216156648936312…95911387031124694601
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
2.019 Γ— 10⁹⁹(100-digit number)
20190432313297872624…91822774062249389199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.019 Γ— 10⁹⁹(100-digit number)
20190432313297872624…91822774062249389201
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
4.038 Γ— 10⁹⁹(100-digit number)
40380864626595745248…83645548124498778399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.038 Γ— 10⁹⁹(100-digit number)
40380864626595745248…83645548124498778401
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 186199

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 da7cddff5880bb600e233fb77ba7e3fb9769d2507cf96d41d8d467c2f6664238

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 #186,199 on Chainz β†—
Circulating Supply:57,643,925 XPMΒ·at block #6,799,982 Β· updates every 60s
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