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Home/Chain Registry/Block #1,682,106

Block #1,682,106

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2016, 6:50:05 PM Β· Difficulty 10.7185 Β· 5,151,806 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0c9425b17c030b34ca60d9877fe7a8d49f4f302d86ff3e34446cb06d145ea500
View on Chainz β†—

Difficulty

10.718514

Transactions

1

Size

199 B

Version

2

Bits

0ab7f08c

Nonce

892,555,977

Timestamp

7/20/2016, 6:50:05 PM

Confirmations

5,151,806

Merkle Root

a740566e67ba07ede172420b51bf375f085e0649b327d26459402b4ff8dad27f
Transactions (1)
Coinbasea740566e67ba07…402b4ff8dad27f
1 in β†’ 1 out8.6900 XPM109 B
AabVLBCw…qpMM89wY
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.

7.401 Γ— 10⁹⁴(95-digit number)
74018861770040689237…25992572632619401120
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
7.401 Γ— 10⁹⁴(95-digit number)
74018861770040689237…25992572632619401119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.401 Γ— 10⁹⁴(95-digit number)
74018861770040689237…25992572632619401121
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
1.480 Γ— 10⁹⁡(96-digit number)
14803772354008137847…51985145265238802239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.480 Γ— 10⁹⁡(96-digit number)
14803772354008137847…51985145265238802241
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
2.960 Γ— 10⁹⁡(96-digit number)
29607544708016275695…03970290530477604479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.960 Γ— 10⁹⁡(96-digit number)
29607544708016275695…03970290530477604481
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
5.921 Γ— 10⁹⁡(96-digit number)
59215089416032551390…07940581060955208959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.921 Γ— 10⁹⁡(96-digit number)
59215089416032551390…07940581060955208961
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
1.184 Γ— 10⁹⁢(97-digit number)
11843017883206510278…15881162121910417919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.184 Γ— 10⁹⁢(97-digit number)
11843017883206510278…15881162121910417921
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 1682106

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 0c9425b17c030b34ca60d9877fe7a8d49f4f302d86ff3e34446cb06d145ea500

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 #1,682,106 on Chainz β†—
Circulating Supply:57,915,521 XPMΒ·at block #6,833,911 Β· updates every 60s
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