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Home/Chain Registry/Block #2,286,172

Block #2,286,172

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2017, 9:01:53 AM Β· Difficulty 10.9556 Β· 4,545,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bd2dc82cbd3c72f2214b0b87a708c1ff1f70144adf1ec6f7c53ac00e63b99055
View on Chainz β†—

Difficulty

10.955580

Transactions

1

Size

200 B

Version

2

Bits

0af4a0e8

Nonce

1,507,067,410

Timestamp

9/7/2017, 9:01:53 AM

Confirmations

4,545,111

Merkle Root

c578402ac82b740c5c0f32c6506fc6340859b3ef0a01607bddbf276c17d4c4fc
Transactions (1)
Coinbasec578402ac82b74…bf276c17d4c4fc
1 in β†’ 1 out8.3200 XPM110 B
AQhzgTqk…fT8A8LAv
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.

6.369 Γ— 10⁹⁡(96-digit number)
63694570642880443947…81533426698434626560
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
6.369 Γ— 10⁹⁡(96-digit number)
63694570642880443947…81533426698434626559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.369 Γ— 10⁹⁡(96-digit number)
63694570642880443947…81533426698434626561
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
1.273 Γ— 10⁹⁢(97-digit number)
12738914128576088789…63066853396869253119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.273 Γ— 10⁹⁢(97-digit number)
12738914128576088789…63066853396869253121
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
2.547 Γ— 10⁹⁢(97-digit number)
25477828257152177578…26133706793738506239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.547 Γ— 10⁹⁢(97-digit number)
25477828257152177578…26133706793738506241
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
5.095 Γ— 10⁹⁢(97-digit number)
50955656514304355157…52267413587477012479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.095 Γ— 10⁹⁢(97-digit number)
50955656514304355157…52267413587477012481
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
1.019 Γ— 10⁹⁷(98-digit number)
10191131302860871031…04534827174954024959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.019 Γ— 10⁹⁷(98-digit number)
10191131302860871031…04534827174954024961
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
2.038 Γ— 10⁹⁷(98-digit number)
20382262605721742063…09069654349908049919
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 2286172

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 bd2dc82cbd3c72f2214b0b87a708c1ff1f70144adf1ec6f7c53ac00e63b99055

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 #2,286,172 on Chainz β†—
Circulating Supply:57,894,409 XPMΒ·at block #6,831,282 Β· updates every 60s
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