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Home/Chain Registry/Block #1,692,307

Block #1,692,307

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/28/2016, 6:41:42 AM Β· Difficulty 10.6839 Β· 5,138,341 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
74be18e8d3a9c8ca8726b6c86b3e8868470fcfc453f9058f2cdbeabafe10dc2a
View on Chainz β†—

Difficulty

10.683938

Transactions

1

Size

199 B

Version

2

Bits

0aaf1695

Nonce

550,263,829

Timestamp

7/28/2016, 6:41:42 AM

Confirmations

5,138,341

Merkle Root

55415741f01b57138f4962a631716732d727e1e30eba76cde5ce5edc02c719fe
Transactions (1)
Coinbase55415741f01b57…ce5edc02c719fe
1 in β†’ 1 out8.7500 XPM109 B
AGz2yHdy…hyz2D6T2
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.

3.387 Γ— 10⁹⁡(96-digit number)
33872785992921218794…84817753103471664640
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
3.387 Γ— 10⁹⁡(96-digit number)
33872785992921218794…84817753103471664639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.387 Γ— 10⁹⁡(96-digit number)
33872785992921218794…84817753103471664641
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
6.774 Γ— 10⁹⁡(96-digit number)
67745571985842437588…69635506206943329279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.774 Γ— 10⁹⁡(96-digit number)
67745571985842437588…69635506206943329281
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
1.354 Γ— 10⁹⁢(97-digit number)
13549114397168487517…39271012413886658559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.354 Γ— 10⁹⁢(97-digit number)
13549114397168487517…39271012413886658561
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
2.709 Γ— 10⁹⁢(97-digit number)
27098228794336975035…78542024827773317119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.709 Γ— 10⁹⁢(97-digit number)
27098228794336975035…78542024827773317121
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
5.419 Γ— 10⁹⁢(97-digit number)
54196457588673950070…57084049655546634239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.419 Γ— 10⁹⁢(97-digit number)
54196457588673950070…57084049655546634241
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 1692307

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 74be18e8d3a9c8ca8726b6c86b3e8868470fcfc453f9058f2cdbeabafe10dc2a

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 #1,692,307 on Chainz β†—
Circulating Supply:57,889,309 XPMΒ·at block #6,830,647 Β· updates every 60s
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