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Home/Chain Registry/Block #2,656,272

Block #2,656,272

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2018, 10:39:16 PM Β· Difficulty 11.6914 Β· 4,186,984 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9574da874bbb26550b9c766b3d6cb2ee10cb46e1ac285129535982b4ac872e65
View on Chainz β†—

Difficulty

11.691370

Transactions

1

Size

200 B

Version

2

Bits

0bb0fda5

Nonce

258,042,122

Timestamp

5/10/2018, 10:39:16 PM

Confirmations

4,186,984

Merkle Root

3fd6d1ec5d50eb78c237606d0d9358c0d7d7013662f38e6cee43e38226ccdd30
Transactions (1)
Coinbase3fd6d1ec5d50eb…43e38226ccdd30
1 in β†’ 1 out7.3000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

6.354 Γ— 10⁹⁴(95-digit number)
63549326828884639796…49688018977243147520
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
6.354 Γ— 10⁹⁴(95-digit number)
63549326828884639796…49688018977243147519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.354 Γ— 10⁹⁴(95-digit number)
63549326828884639796…49688018977243147521
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
1.270 Γ— 10⁹⁡(96-digit number)
12709865365776927959…99376037954486295039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.270 Γ— 10⁹⁡(96-digit number)
12709865365776927959…99376037954486295041
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
2.541 Γ— 10⁹⁡(96-digit number)
25419730731553855918…98752075908972590079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.541 Γ— 10⁹⁡(96-digit number)
25419730731553855918…98752075908972590081
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
5.083 Γ— 10⁹⁡(96-digit number)
50839461463107711836…97504151817945180159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.083 Γ— 10⁹⁡(96-digit number)
50839461463107711836…97504151817945180161
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
1.016 Γ— 10⁹⁢(97-digit number)
10167892292621542367…95008303635890360319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.016 Γ— 10⁹⁢(97-digit number)
10167892292621542367…95008303635890360321
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
2.033 Γ— 10⁹⁢(97-digit number)
20335784585243084734…90016607271780720639
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 2656272

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 9574da874bbb26550b9c766b3d6cb2ee10cb46e1ac285129535982b4ac872e65

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 #2,656,272 on Chainz β†—
Circulating Supply:57,990,425 XPMΒ·at block #6,843,255 Β· updates every 60s
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