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Home/Chain Registry/Block #2,170,792

Block #2,170,792

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2017, 5:24:13 PM Β· Difficulty 10.9037 Β· 4,670,429 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ed1b4473d3f7804d3a76a5ffa784c20260a8e7230522ef423ee5887af77d1781
View on Chainz β†—

Difficulty

10.903739

Transactions

1

Size

199 B

Version

2

Bits

0ae75b72

Nonce

203,645,452

Timestamp

6/21/2017, 5:24:13 PM

Confirmations

4,670,429

Merkle Root

36c472dcfc35d3503b520e4638797b6367524a55ba47681af36c381c531e535b
Transactions (1)
Coinbase36c472dcfc35d3…6c381c531e535b
1 in β†’ 1 out8.4000 XPM109 B
AFy7E7AF…aV5ocHzb
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.

1.573 Γ— 10⁹⁡(96-digit number)
15737611437740455741…21520275956283226240
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
1.573 Γ— 10⁹⁡(96-digit number)
15737611437740455741…21520275956283226239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.573 Γ— 10⁹⁡(96-digit number)
15737611437740455741…21520275956283226241
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
3.147 Γ— 10⁹⁡(96-digit number)
31475222875480911483…43040551912566452479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.147 Γ— 10⁹⁡(96-digit number)
31475222875480911483…43040551912566452481
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
6.295 Γ— 10⁹⁡(96-digit number)
62950445750961822966…86081103825132904959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.295 Γ— 10⁹⁡(96-digit number)
62950445750961822966…86081103825132904961
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
1.259 Γ— 10⁹⁢(97-digit number)
12590089150192364593…72162207650265809919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.259 Γ— 10⁹⁢(97-digit number)
12590089150192364593…72162207650265809921
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
2.518 Γ— 10⁹⁢(97-digit number)
25180178300384729186…44324415300531619839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.518 Γ— 10⁹⁢(97-digit number)
25180178300384729186…44324415300531619841
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 2170792

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 ed1b4473d3f7804d3a76a5ffa784c20260a8e7230522ef423ee5887af77d1781

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 #2,170,792 on Chainz β†—
Circulating Supply:57,974,125 XPMΒ·at block #6,841,220 Β· updates every 60s
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