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Block #188,902

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/1/2013, 11:56:41 AM Β· Difficulty 9.8713 Β· 6,611,771 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4498cccaabe9f73bb8bd99dbf5b7ac0f2db3582eb1436dce33444ac10fab0c4
View on Chainz β†—

Height

#188,902

Difficulty

9.871285

Transactions

1

Size

199 B

Version

2

Bits

09df0c88

Nonce

41,812

Timestamp

10/1/2013, 11:56:41 AM

Confirmations

6,611,771

Merkle Root

f21759b234daa52bbc7b6c2e86697e84b97cef3d5a8681fea1b936ac399f7a4d
Transactions (1)
Coinbasef21759b234daa5…b936ac399f7a4d
1 in β†’ 1 out10.2500 XPM109 B
AZZPbi1u…YhPG9rbe
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.

3.870 Γ— 10⁹⁡(96-digit number)
38703381643016921315…27363224034137335760
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
3.870 Γ— 10⁹⁡(96-digit number)
38703381643016921315…27363224034137335759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.870 Γ— 10⁹⁡(96-digit number)
38703381643016921315…27363224034137335761
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
7.740 Γ— 10⁹⁡(96-digit number)
77406763286033842630…54726448068274671519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.740 Γ— 10⁹⁡(96-digit number)
77406763286033842630…54726448068274671521
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
1.548 Γ— 10⁹⁢(97-digit number)
15481352657206768526…09452896136549343039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.548 Γ— 10⁹⁢(97-digit number)
15481352657206768526…09452896136549343041
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
3.096 Γ— 10⁹⁢(97-digit number)
30962705314413537052…18905792273098686079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.096 Γ— 10⁹⁢(97-digit number)
30962705314413537052…18905792273098686081
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
6.192 Γ— 10⁹⁢(97-digit number)
61925410628827074104…37811584546197372159
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 188902

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 b4498cccaabe9f73bb8bd99dbf5b7ac0f2db3582eb1436dce33444ac10fab0c4

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 #188,902 on Chainz β†—
Circulating Supply:57,649,448 XPMΒ·at block #6,800,672 Β· updates every 60s
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