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Home/Chain Registry/Block #2,272,095

Block #2,272,095

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 4:32:32 PM Β· Difficulty 10.9540 Β· 4,570,317 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2d382168318e4ba6840b5359d9b5ec7a4fd79dfec3c32e95170873e1f133e60b
View on Chainz β†—

Difficulty

10.954010

Transactions

2

Size

609 B

Version

2

Bits

0af439fd

Nonce

201,770,621

Timestamp

8/28/2017, 4:32:32 PM

Confirmations

4,570,317

Merkle Root

1e7b4dcb3a638c7e515d49046905643f6790b9dfc390d4be44b4b604aa78bec5
Transactions (2)
Coinbasedbfd4439f03579…7f1d5fc4b4463c
1 in β†’ 1 out8.3300 XPM109 B
AW5zNBZX…1aajSXHZ
bcff1db785cf48…3181ca928a78bf
2 in β†’ 3 out1572.7861 XPM410 B
ASnzm9S9…A3PBVhJEAJHMr1yt…5D7T6WWzAPCLwsZN…Y9nxkbdb
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.

1.482 Γ— 10⁹⁡(96-digit number)
14826715259179063436…10253548699892512240
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
1.482 Γ— 10⁹⁡(96-digit number)
14826715259179063436…10253548699892512239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.482 Γ— 10⁹⁡(96-digit number)
14826715259179063436…10253548699892512241
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
2.965 Γ— 10⁹⁡(96-digit number)
29653430518358126873…20507097399785024479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.965 Γ— 10⁹⁡(96-digit number)
29653430518358126873…20507097399785024481
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
5.930 Γ— 10⁹⁡(96-digit number)
59306861036716253746…41014194799570048959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.930 Γ— 10⁹⁡(96-digit number)
59306861036716253746…41014194799570048961
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
1.186 Γ— 10⁹⁢(97-digit number)
11861372207343250749…82028389599140097919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.186 Γ— 10⁹⁢(97-digit number)
11861372207343250749…82028389599140097921
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
2.372 Γ— 10⁹⁢(97-digit number)
23722744414686501498…64056779198280195839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.372 Γ— 10⁹⁢(97-digit number)
23722744414686501498…64056779198280195841
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
4.744 Γ— 10⁹⁢(97-digit number)
47445488829373002997…28113558396560391679
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 2272095

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 2d382168318e4ba6840b5359d9b5ec7a4fd79dfec3c32e95170873e1f133e60b

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 #2,272,095 on Chainz β†—
Circulating Supply:57,983,709 XPMΒ·at block #6,842,411 Β· updates every 60s
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