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Home/Chain Registry/Block #1,981,548

Block #1,981,548

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/13/2017, 9:58:03 AM Β· Difficulty 10.7536 Β· 4,861,284 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b8ced2163b4217d21a176f7c9835523462206d50dc87da9cd52b4a034e942425
View on Chainz β†—

Difficulty

10.753635

Transactions

1

Size

243 B

Version

2

Bits

0ac0ee3d

Nonce

144,177,509

Timestamp

2/13/2017, 9:58:03 AM

Confirmations

4,861,284

Merkle Root

ae0f436aba3fa7034a01ffa0ff38b97f0c005abeb328f7b7d608b90b3d234ad9
Transactions (1)
Coinbaseae0f436aba3fa7…08b90b3d234ad9
1 in β†’ 2 out8.6300 XPM152 B
Abwunkt2…zS3pHkCHAXbk7f7A…Tx7JECPG
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.

1.816 Γ— 10⁹⁢(97-digit number)
18168406386281400242…20792912458416602720
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
1.816 Γ— 10⁹⁢(97-digit number)
18168406386281400242…20792912458416602719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.816 Γ— 10⁹⁢(97-digit number)
18168406386281400242…20792912458416602721
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
3.633 Γ— 10⁹⁢(97-digit number)
36336812772562800485…41585824916833205439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.633 Γ— 10⁹⁢(97-digit number)
36336812772562800485…41585824916833205441
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
7.267 Γ— 10⁹⁢(97-digit number)
72673625545125600971…83171649833666410879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.267 Γ— 10⁹⁢(97-digit number)
72673625545125600971…83171649833666410881
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
1.453 Γ— 10⁹⁷(98-digit number)
14534725109025120194…66343299667332821759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.453 Γ— 10⁹⁷(98-digit number)
14534725109025120194…66343299667332821761
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
2.906 Γ— 10⁹⁷(98-digit number)
29069450218050240388…32686599334665643519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.906 Γ— 10⁹⁷(98-digit number)
29069450218050240388…32686599334665643521
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 1981548

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 b8ced2163b4217d21a176f7c9835523462206d50dc87da9cd52b4a034e942425

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 #1,981,548 on Chainz β†—
Circulating Supply:57,986,999 XPMΒ·at block #6,842,831 Β· updates every 60s
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