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Block #849,282

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/11/2014, 5:22:02 PM Β· Difficulty 10.9713 Β· 5,993,623 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
acd27eb9a337dc434137ed59da1d97f9cad1ff53a063e4f2a639d18347053f2b
View on Chainz β†—

Height

#849,282

Difficulty

10.971270

Transactions

1

Size

208 B

Version

2

Bits

0af8a52b

Nonce

1,092,828,515

Timestamp

12/11/2014, 5:22:02 PM

Confirmations

5,993,623

Merkle Root

12ec223f638324f547a7fbb26c450b4118274f580d3b40765040837b2d49b16b
Transactions (1)
Coinbase12ec223f638324…40837b2d49b16b
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.

7.270 Γ— 10⁹⁹(100-digit number)
72708523008532688517…35595277163580948480
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
7.270 Γ— 10⁹⁹(100-digit number)
72708523008532688517…35595277163580948479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.270 Γ— 10⁹⁹(100-digit number)
72708523008532688517…35595277163580948481
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
1.454 Γ— 10¹⁰⁰(101-digit number)
14541704601706537703…71190554327161896959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.454 Γ— 10¹⁰⁰(101-digit number)
14541704601706537703…71190554327161896961
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
2.908 Γ— 10¹⁰⁰(101-digit number)
29083409203413075407…42381108654323793919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.908 Γ— 10¹⁰⁰(101-digit number)
29083409203413075407…42381108654323793921
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
5.816 Γ— 10¹⁰⁰(101-digit number)
58166818406826150814…84762217308647587839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.816 Γ— 10¹⁰⁰(101-digit number)
58166818406826150814…84762217308647587841
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
1.163 Γ— 10¹⁰¹(102-digit number)
11633363681365230162…69524434617295175679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.163 Γ— 10¹⁰¹(102-digit number)
11633363681365230162…69524434617295175681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.326 Γ— 10¹⁰¹(102-digit number)
23266727362730460325…39048869234590351359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 849282

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 acd27eb9a337dc434137ed59da1d97f9cad1ff53a063e4f2a639d18347053f2b

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 #849,282 on Chainz β†—
Circulating Supply:57,987,587 XPMΒ·at block #6,842,904 Β· updates every 60s
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