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Block #2,276,512

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2017, 4:04:45 PM Β· Difficulty 10.9553 Β· 4,554,443 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd957961c8ca73b80cec363b121b9e094398cebe7be607251af9932b70c578b3
View on Chainz β†—

Difficulty

10.955261

Transactions

1

Size

200 B

Version

2

Bits

0af48bf6

Nonce

304,204,489

Timestamp

8/31/2017, 4:04:45 PM

Confirmations

4,554,443

Merkle Root

131c82facddd18d26f59228bf287b7b35e746326ddcc0284aeb5a0da56ef49ca
Transactions (1)
Coinbase131c82facddd18…b5a0da56ef49ca
1 in β†’ 1 out8.3200 XPM110 B
AZqkT4di…qgyBKbDT
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.

4.371 Γ— 10⁹³(94-digit number)
43714712430119311005…58578756105501573120
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
4.371 Γ— 10⁹³(94-digit number)
43714712430119311005…58578756105501573119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.371 Γ— 10⁹³(94-digit number)
43714712430119311005…58578756105501573121
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
8.742 Γ— 10⁹³(94-digit number)
87429424860238622010…17157512211003146239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.742 Γ— 10⁹³(94-digit number)
87429424860238622010…17157512211003146241
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
1.748 Γ— 10⁹⁴(95-digit number)
17485884972047724402…34315024422006292479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.748 Γ— 10⁹⁴(95-digit number)
17485884972047724402…34315024422006292481
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
3.497 Γ— 10⁹⁴(95-digit number)
34971769944095448804…68630048844012584959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.497 Γ— 10⁹⁴(95-digit number)
34971769944095448804…68630048844012584961
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
6.994 Γ— 10⁹⁴(95-digit number)
69943539888190897608…37260097688025169919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.994 Γ— 10⁹⁴(95-digit number)
69943539888190897608…37260097688025169921
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
1.398 Γ— 10⁹⁡(96-digit number)
13988707977638179521…74520195376050339839
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 2276512

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 fd957961c8ca73b80cec363b121b9e094398cebe7be607251af9932b70c578b3

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 #2,276,512 on Chainz β†—
Circulating Supply:57,891,776 XPMΒ·at block #6,830,954 Β· updates every 60s
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