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Home/Chain Registry/Block #2,831,633

Block #2,831,633

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2018, 11:25:05 AM Β· Difficulty 11.7174 Β· 4,011,702 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2f23ffbf2d3393dc383a440912c43dcfae0f55fb5520b9aa1de84a07732a34c2
View on Chainz β†—

Difficulty

11.717434

Transactions

1

Size

200 B

Version

2

Bits

0bb7a9c4

Nonce

4,820,515

Timestamp

9/9/2018, 11:25:05 AM

Confirmations

4,011,702

Merkle Root

c53899d7df659186454ea2fb61a6fc5551c0e6a3db8d1bb97073e63ee9297b76
Transactions (1)
Coinbasec53899d7df6591…73e63ee9297b76
1 in β†’ 1 out7.2700 XPM110 B
AcHUBDcx…hHKavFQL
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.

6.135 Γ— 10⁹⁡(96-digit number)
61354358235435532990…78210197693548820640
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
6.135 Γ— 10⁹⁡(96-digit number)
61354358235435532990…78210197693548820639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.135 Γ— 10⁹⁡(96-digit number)
61354358235435532990…78210197693548820641
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
1.227 Γ— 10⁹⁢(97-digit number)
12270871647087106598…56420395387097641279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.227 Γ— 10⁹⁢(97-digit number)
12270871647087106598…56420395387097641281
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
2.454 Γ— 10⁹⁢(97-digit number)
24541743294174213196…12840790774195282559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.454 Γ— 10⁹⁢(97-digit number)
24541743294174213196…12840790774195282561
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
4.908 Γ— 10⁹⁢(97-digit number)
49083486588348426392…25681581548390565119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.908 Γ— 10⁹⁢(97-digit number)
49083486588348426392…25681581548390565121
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
9.816 Γ— 10⁹⁢(97-digit number)
98166973176696852785…51363163096781130239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.816 Γ— 10⁹⁢(97-digit number)
98166973176696852785…51363163096781130241
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
1.963 Γ— 10⁹⁷(98-digit number)
19633394635339370557…02726326193562260479
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 2831633

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 2f23ffbf2d3393dc383a440912c43dcfae0f55fb5520b9aa1de84a07732a34c2

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 #2,831,633 on Chainz β†—
Circulating Supply:57,991,042 XPMΒ·at block #6,843,334 Β· updates every 60s
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