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Block #844,653

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/8/2014, 6:44:53 AM Β· Difficulty 10.9729 Β· 5,980,016 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70c21a4a461b11f97cd5d3febfe7a3c087a340114822dc348d44da51f5ea3908
View on Chainz β†—

Height

#844,653

Difficulty

10.972946

Transactions

1

Size

208 B

Version

2

Bits

0af91305

Nonce

969,410,805

Timestamp

12/8/2014, 6:44:53 AM

Confirmations

5,980,016

Merkle Root

21f77fe5b18eddf3a73ea8457551cc4852a6b1e43206c956e91d9c705103e971
Transactions (1)
Coinbase21f77fe5b18edd…1d9c705103e971
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.154 Γ— 10⁹⁸(99-digit number)
21544984580966884862…41990043971895640640
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
2.154 Γ— 10⁹⁸(99-digit number)
21544984580966884862…41990043971895640639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.154 Γ— 10⁹⁸(99-digit number)
21544984580966884862…41990043971895640641
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
4.308 Γ— 10⁹⁸(99-digit number)
43089969161933769725…83980087943791281279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.308 Γ— 10⁹⁸(99-digit number)
43089969161933769725…83980087943791281281
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
8.617 Γ— 10⁹⁸(99-digit number)
86179938323867539451…67960175887582562559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.617 Γ— 10⁹⁸(99-digit number)
86179938323867539451…67960175887582562561
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
1.723 Γ— 10⁹⁹(100-digit number)
17235987664773507890…35920351775165125119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.723 Γ— 10⁹⁹(100-digit number)
17235987664773507890…35920351775165125121
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
3.447 Γ— 10⁹⁹(100-digit number)
34471975329547015780…71840703550330250239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.447 Γ— 10⁹⁹(100-digit number)
34471975329547015780…71840703550330250241
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 844653

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 70c21a4a461b11f97cd5d3febfe7a3c087a340114822dc348d44da51f5ea3908

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 #844,653 on Chainz β†—
Circulating Supply:57,841,416 XPMΒ·at block #6,824,668 Β· updates every 60s
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