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Home/Chain Registry/Block #1,891,659

Block #1,891,659

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2016, 5:33:58 AM Β· Difficulty 10.7325 Β· 4,953,990 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a6d589db0203d81b0d7e58f776c2e3949a163be18d7c069600975709c9081768
View on Chainz β†—

Difficulty

10.732542

Transactions

2

Size

874 B

Version

2

Bits

0abb87e1

Nonce

1,406,121,686

Timestamp

12/13/2016, 5:33:58 AM

Confirmations

4,953,990

Merkle Root

44f4f852be3390db0b0cc07365a3ec988c54512afb03502f9a7b299e8071df8b
Transactions (2)
Coinbase8547c287dddbe8…20766b104d3dda
1 in β†’ 1 out8.6800 XPM109 B
AZEjCGgT…8ytB8s83
900a688a610064…a5a5e386f2fa51
4 in β†’ 2 out2.4570 XPM674 B
ASMMZz4E…7FeHYYcpAZXQSnLT…d7cgMEFD
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.

6.863 Γ— 10⁹⁢(97-digit number)
68639692912504749935…87290944249960284160
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
6.863 Γ— 10⁹⁢(97-digit number)
68639692912504749935…87290944249960284159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.863 Γ— 10⁹⁢(97-digit number)
68639692912504749935…87290944249960284161
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
1.372 Γ— 10⁹⁷(98-digit number)
13727938582500949987…74581888499920568319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.372 Γ— 10⁹⁷(98-digit number)
13727938582500949987…74581888499920568321
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
2.745 Γ— 10⁹⁷(98-digit number)
27455877165001899974…49163776999841136639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.745 Γ— 10⁹⁷(98-digit number)
27455877165001899974…49163776999841136641
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
5.491 Γ— 10⁹⁷(98-digit number)
54911754330003799948…98327553999682273279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.491 Γ— 10⁹⁷(98-digit number)
54911754330003799948…98327553999682273281
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
1.098 Γ— 10⁹⁸(99-digit number)
10982350866000759989…96655107999364546559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.098 Γ— 10⁹⁸(99-digit number)
10982350866000759989…96655107999364546561
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 1891659

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 a6d589db0203d81b0d7e58f776c2e3949a163be18d7c069600975709c9081768

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 #1,891,659 on Chainz β†—
Circulating Supply:58,009,641 XPMΒ·at block #6,845,648 Β· updates every 60s
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