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Block #116,946

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/14/2013, 5:56:13 PM Β· Difficulty 9.7502 Β· 6,708,366 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8365380679341fa1a512e4cda9f2eb7d140e95b5dfb49cbb374cee1419eb6835
View on Chainz β†—

Height

#116,946

Difficulty

9.750207

Transactions

1

Size

201 B

Version

2

Bits

09c00d90

Nonce

49,340

Timestamp

8/14/2013, 5:56:13 PM

Confirmations

6,708,366

Merkle Root

6dac8eeb608cf64ba4665b406846ae4c079b87e0d358ba719669aff4694c280b
Transactions (1)
Coinbase6dac8eeb608cf6…69aff4694c280b
1 in β†’ 1 out10.5000 XPM109 B
AJbVrJa8…BfoUdsof
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.

4.331 Γ— 10⁹⁸(99-digit number)
43310645894012211811…16523216981665637200
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
4.331 Γ— 10⁹⁸(99-digit number)
43310645894012211811…16523216981665637199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.331 Γ— 10⁹⁸(99-digit number)
43310645894012211811…16523216981665637201
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
8.662 Γ— 10⁹⁸(99-digit number)
86621291788024423623…33046433963331274399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.662 Γ— 10⁹⁸(99-digit number)
86621291788024423623…33046433963331274401
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
1.732 Γ— 10⁹⁹(100-digit number)
17324258357604884724…66092867926662548799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.732 Γ— 10⁹⁹(100-digit number)
17324258357604884724…66092867926662548801
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
3.464 Γ— 10⁹⁹(100-digit number)
34648516715209769449…32185735853325097599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.464 Γ— 10⁹⁹(100-digit number)
34648516715209769449…32185735853325097601
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
6.929 Γ— 10⁹⁹(100-digit number)
69297033430419538898…64371471706650195199
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 116946

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 8365380679341fa1a512e4cda9f2eb7d140e95b5dfb49cbb374cee1419eb6835

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 #116,946 on Chainz β†—
Circulating Supply:57,846,599 XPMΒ·at block #6,825,311 Β· updates every 60s
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