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Block #812,137

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/15/2014, 12:39:32 PM Β· Difficulty 10.9731 Β· 6,013,407 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
80ac34d447d75d71b2e7e7b29e6b13b3e47e1b3ae6daefa071989bcb66aca481
View on Chainz β†—

Height

#812,137

Difficulty

10.973123

Transactions

2

Size

432 B

Version

2

Bits

0af91e93

Nonce

32,831,366

Timestamp

11/15/2014, 12:39:32 PM

Confirmations

6,013,407

Merkle Root

64fc81f7feb65b5722fd134c5862130db0f7880a2c7c22aef4f1b17d810dd421
Transactions (2)
Coinbase033c6e78ee7efe…b485dccf765d4e
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
019d6e66d4a334…45daef02d8d1c6
1 in β†’ 2 out0.6215 XPM226 B
AQN7WEAG…rgot6XjaAZzg2AXj…gZMnX8Wy
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.

1.366 Γ— 10⁹⁡(96-digit number)
13666362639077633656…41618781785458676480
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
1.366 Γ— 10⁹⁡(96-digit number)
13666362639077633656…41618781785458676479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.366 Γ— 10⁹⁡(96-digit number)
13666362639077633656…41618781785458676481
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
2.733 Γ— 10⁹⁡(96-digit number)
27332725278155267313…83237563570917352959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.733 Γ— 10⁹⁡(96-digit number)
27332725278155267313…83237563570917352961
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
5.466 Γ— 10⁹⁡(96-digit number)
54665450556310534626…66475127141834705919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.466 Γ— 10⁹⁡(96-digit number)
54665450556310534626…66475127141834705921
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
1.093 Γ— 10⁹⁢(97-digit number)
10933090111262106925…32950254283669411839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.093 Γ— 10⁹⁢(97-digit number)
10933090111262106925…32950254283669411841
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
2.186 Γ— 10⁹⁢(97-digit number)
21866180222524213850…65900508567338823679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.186 Γ— 10⁹⁢(97-digit number)
21866180222524213850…65900508567338823681
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 812137

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 80ac34d447d75d71b2e7e7b29e6b13b3e47e1b3ae6daefa071989bcb66aca481

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 #812,137 on Chainz β†—
Circulating Supply:57,848,451 XPMΒ·at block #6,825,543 Β· updates every 60s
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