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Block #118,295

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2013, 4:27:42 PM Β· Difficulty 9.7503 Β· 6,683,205 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fbac44b67de28d6dd9ceac043461988f8d0eb016474043e22d5bf08da52cdb16
View on Chainz β†—

Height

#118,295

Difficulty

9.750314

Transactions

1

Size

203 B

Version

2

Bits

09c0148c

Nonce

457,934

Timestamp

8/15/2013, 4:27:42 PM

Confirmations

6,683,205

Merkle Root

55887280fc29d74d1397138fcf758c5e845b79f6bb6cb860579888496e3d9f07
Transactions (1)
Coinbase55887280fc29d7…9888496e3d9f07
1 in β†’ 1 out10.5000 XPM112 B
AT5A2KL6…CT16n6i2
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.

1.503 Γ— 10⁹⁸(99-digit number)
15032840193075804539…09045122747908854000
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
1.503 Γ— 10⁹⁸(99-digit number)
15032840193075804539…09045122747908853999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.503 Γ— 10⁹⁸(99-digit number)
15032840193075804539…09045122747908854001
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
3.006 Γ— 10⁹⁸(99-digit number)
30065680386151609079…18090245495817707999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.006 Γ— 10⁹⁸(99-digit number)
30065680386151609079…18090245495817708001
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
6.013 Γ— 10⁹⁸(99-digit number)
60131360772303218159…36180490991635415999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.013 Γ— 10⁹⁸(99-digit number)
60131360772303218159…36180490991635416001
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
1.202 Γ— 10⁹⁹(100-digit number)
12026272154460643631…72360981983270831999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.202 Γ— 10⁹⁹(100-digit number)
12026272154460643631…72360981983270832001
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
2.405 Γ— 10⁹⁹(100-digit number)
24052544308921287263…44721963966541663999
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 118295

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 fbac44b67de28d6dd9ceac043461988f8d0eb016474043e22d5bf08da52cdb16

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 #118,295 on Chainz β†—
Circulating Supply:57,656,073 XPMΒ·at block #6,801,499 Β· updates every 60s
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