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Block #2,047,644

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/1/2017, 4:48:46 AM Β· Difficulty 10.6876 Β· 4,791,616 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e5333e6e89fe41126ea7f84e78998f72fd4fa6979bb9f5217ab8699454d518bc
View on Chainz β†—

Difficulty

10.687580

Transactions

2

Size

1.28 KB

Version

2

Bits

0ab0053d

Nonce

688,246,564

Timestamp

4/1/2017, 4:48:46 AM

Confirmations

4,791,616

Merkle Root

c0f19b43ba3d9cae70f60a52540fcbf03e25b08820eb970f2ea17219fafa41bc
Transactions (2)
Coinbase419105a3198b60…5a31b88ed0defd
1 in β†’ 1 out8.7600 XPM109 B
ASDD8f2J…BP1XSYbs
d4c340fdf735ac…e9be683159b0cc
7 in β†’ 2 out1348.9504 XPM1.09 KB
AcFnNkyp…abCsvUgvAY7QT1Zq…2vLS6thV
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.

1.878 Γ— 10⁹⁴(95-digit number)
18788529362809461430…71494922990159708160
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
1.878 Γ— 10⁹⁴(95-digit number)
18788529362809461430…71494922990159708159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.878 Γ— 10⁹⁴(95-digit number)
18788529362809461430…71494922990159708161
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
3.757 Γ— 10⁹⁴(95-digit number)
37577058725618922860…42989845980319416319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.757 Γ— 10⁹⁴(95-digit number)
37577058725618922860…42989845980319416321
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
7.515 Γ— 10⁹⁴(95-digit number)
75154117451237845721…85979691960638832639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.515 Γ— 10⁹⁴(95-digit number)
75154117451237845721…85979691960638832641
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
1.503 Γ— 10⁹⁡(96-digit number)
15030823490247569144…71959383921277665279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.503 Γ— 10⁹⁡(96-digit number)
15030823490247569144…71959383921277665281
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
3.006 Γ— 10⁹⁡(96-digit number)
30061646980495138288…43918767842555330559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.006 Γ— 10⁹⁡(96-digit number)
30061646980495138288…43918767842555330561
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 2047644

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 e5333e6e89fe41126ea7f84e78998f72fd4fa6979bb9f5217ab8699454d518bc

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 #2,047,644 on Chainz β†—
Circulating Supply:57,958,362 XPMΒ·at block #6,839,259 Β· updates every 60s
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