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Home/Chain Registry/Block #1,294,310

Block #1,294,310

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/22/2015, 6:58:10 PM Β· Difficulty 10.8613 Β· 5,501,277 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b25bac3124ef4b4b7d94ab28803eddb45225518b963f2ca099d0ee986e3bbea
View on Chainz β†—

Difficulty

10.861314

Transactions

1

Size

201 B

Version

2

Bits

0adc7f10

Nonce

895,404,348

Timestamp

10/22/2015, 6:58:10 PM

Confirmations

5,501,277

Merkle Root

2899702a4a1fe3fb2b4f70453a69ba641cda06f933bd7e1bb01d77cee0e55070
Transactions (1)
Coinbase2899702a4a1fe3…1d77cee0e55070
1 in β†’ 1 out8.4600 XPM110 B
AeuDVQmz…cmjwMvdd
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.

8.186 Γ— 10⁹⁢(97-digit number)
81868377524404994482…37572786165121054720
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
8.186 Γ— 10⁹⁢(97-digit number)
81868377524404994482…37572786165121054719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.186 Γ— 10⁹⁢(97-digit number)
81868377524404994482…37572786165121054721
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
1.637 Γ— 10⁹⁷(98-digit number)
16373675504880998896…75145572330242109439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.637 Γ— 10⁹⁷(98-digit number)
16373675504880998896…75145572330242109441
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
3.274 Γ— 10⁹⁷(98-digit number)
32747351009761997793…50291144660484218879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.274 Γ— 10⁹⁷(98-digit number)
32747351009761997793…50291144660484218881
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
6.549 Γ— 10⁹⁷(98-digit number)
65494702019523995586…00582289320968437759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.549 Γ— 10⁹⁷(98-digit number)
65494702019523995586…00582289320968437761
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
1.309 Γ— 10⁹⁸(99-digit number)
13098940403904799117…01164578641936875519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.309 Γ— 10⁹⁸(99-digit number)
13098940403904799117…01164578641936875521
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 1294310

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 6b25bac3124ef4b4b7d94ab28803eddb45225518b963f2ca099d0ee986e3bbea

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 #1,294,310 on Chainz β†—
Circulating Supply:57,608,759 XPMΒ·at block #6,795,586 Β· updates every 60s
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