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Home/Chain Registry/Block #2,647,189

Block #2,647,189

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 7:19:35 PM Β· Difficulty 11.7562 Β· 4,184,620 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1265a5da67eb969d0f74844f0b6497dfab10e815b4b0e3a8a43bb432e32a710a
View on Chainz β†—

Difficulty

11.756215

Transactions

2

Size

427 B

Version

2

Bits

0bc1974b

Nonce

1,978,552,786

Timestamp

5/3/2018, 7:19:35 PM

Confirmations

4,184,620

Merkle Root

2dc7a708733b79b21263ef32f378287c5e8b97568a10e1605005ea4cc079f12d
Transactions (2)
Coinbaseb3dfd927cfa6a3…32c3e4b6b9061b
1 in β†’ 1 out7.2300 XPM110 B
AW1TvvVH…SQWhuTbj
2d20f0ac9334f7…fdfc22c6a055c9
1 in β†’ 2 out0.3705 XPM226 B
Abn3ZzFV…7t3ZTAgcAUZX515p…XNb6qVDe
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.

5.951 Γ— 10⁹⁷(98-digit number)
59513499616882130406…97129266321017835520
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
5.951 Γ— 10⁹⁷(98-digit number)
59513499616882130406…97129266321017835519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.951 Γ— 10⁹⁷(98-digit number)
59513499616882130406…97129266321017835521
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
1.190 Γ— 10⁹⁸(99-digit number)
11902699923376426081…94258532642035671039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.190 Γ— 10⁹⁸(99-digit number)
11902699923376426081…94258532642035671041
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
2.380 Γ— 10⁹⁸(99-digit number)
23805399846752852162…88517065284071342079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.380 Γ— 10⁹⁸(99-digit number)
23805399846752852162…88517065284071342081
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
4.761 Γ— 10⁹⁸(99-digit number)
47610799693505704325…77034130568142684159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.761 Γ— 10⁹⁸(99-digit number)
47610799693505704325…77034130568142684161
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
9.522 Γ— 10⁹⁸(99-digit number)
95221599387011408650…54068261136285368319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.522 Γ— 10⁹⁸(99-digit number)
95221599387011408650…54068261136285368321
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
1.904 Γ— 10⁹⁹(100-digit number)
19044319877402281730…08136522272570736639
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 2647189

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 1265a5da67eb969d0f74844f0b6497dfab10e815b4b0e3a8a43bb432e32a710a

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 #2,647,189 on Chainz β†—
Circulating Supply:57,898,587 XPMΒ·at block #6,831,808 Β· updates every 60s
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