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Home/Chain Registry/Block #1,853,195

Block #1,853,195

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/17/2016, 1:43:40 PM Β· Difficulty 10.6371 Β· 4,983,827 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c48feae4e572b00a37f80f2a6822edb87748c11b8ac10a1269e8077fe4725a8
View on Chainz β†—

Difficulty

10.637090

Transactions

1

Size

243 B

Version

2

Bits

0aa31859

Nonce

132,121,724

Timestamp

11/17/2016, 1:43:40 PM

Confirmations

4,983,827

Merkle Root

73402a3b57254224b5051e8856865d25334729291ee66841efec83c395c428fe
Transactions (1)
Coinbase73402a3b572542…ec83c395c428fe
1 in β†’ 2 out8.8200 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

3.964 Γ— 10⁹⁢(97-digit number)
39646842311541548056…99793083244262223360
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
3.964 Γ— 10⁹⁢(97-digit number)
39646842311541548056…99793083244262223359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.964 Γ— 10⁹⁢(97-digit number)
39646842311541548056…99793083244262223361
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
7.929 Γ— 10⁹⁢(97-digit number)
79293684623083096112…99586166488524446719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.929 Γ— 10⁹⁢(97-digit number)
79293684623083096112…99586166488524446721
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
1.585 Γ— 10⁹⁷(98-digit number)
15858736924616619222…99172332977048893439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.585 Γ— 10⁹⁷(98-digit number)
15858736924616619222…99172332977048893441
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
3.171 Γ— 10⁹⁷(98-digit number)
31717473849233238445…98344665954097786879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.171 Γ— 10⁹⁷(98-digit number)
31717473849233238445…98344665954097786881
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
6.343 Γ— 10⁹⁷(98-digit number)
63434947698466476890…96689331908195573759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.343 Γ— 10⁹⁷(98-digit number)
63434947698466476890…96689331908195573761
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
1.268 Γ— 10⁹⁸(99-digit number)
12686989539693295378…93378663816391147519
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 1853195

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 6c48feae4e572b00a37f80f2a6822edb87748c11b8ac10a1269e8077fe4725a8

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 #1,853,195 on Chainz β†—
Circulating Supply:57,940,474 XPMΒ·at block #6,837,021 Β· updates every 60s
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