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Home/Chain Registry/Block #2,571,934

Block #2,571,934

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/18/2018, 7:18:27 AM Β· Difficulty 10.9948 Β· 4,273,719 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
502fb61f5305eb15f13ae3e7975c136592c5e15da8e67dd442797274f30c6399
View on Chainz β†—

Difficulty

10.994792

Transactions

1

Size

200 B

Version

2

Bits

0afeaaae

Nonce

202,284,799

Timestamp

3/18/2018, 7:18:27 AM

Confirmations

4,273,719

Merkle Root

e6cbc4b9dc4a45bb668ead7af37b6ad822319d0ca4a6364e2b396a7f7cff0c97
Transactions (1)
Coinbasee6cbc4b9dc4a45…396a7f7cff0c97
1 in β†’ 1 out8.2600 XPM109 B
AH69gLv6…yjkxcBM7
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.

3.015 Γ— 10⁹⁷(98-digit number)
30150874966368474231…00860618311842944000
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
3.015 Γ— 10⁹⁷(98-digit number)
30150874966368474231…00860618311842943999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.015 Γ— 10⁹⁷(98-digit number)
30150874966368474231…00860618311842944001
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
6.030 Γ— 10⁹⁷(98-digit number)
60301749932736948463…01721236623685887999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.030 Γ— 10⁹⁷(98-digit number)
60301749932736948463…01721236623685888001
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
1.206 Γ— 10⁹⁸(99-digit number)
12060349986547389692…03442473247371775999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.206 Γ— 10⁹⁸(99-digit number)
12060349986547389692…03442473247371776001
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
2.412 Γ— 10⁹⁸(99-digit number)
24120699973094779385…06884946494743551999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.412 Γ— 10⁹⁸(99-digit number)
24120699973094779385…06884946494743552001
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
4.824 Γ— 10⁹⁸(99-digit number)
48241399946189558771…13769892989487103999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.824 Γ— 10⁹⁸(99-digit number)
48241399946189558771…13769892989487104001
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 2571934

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 502fb61f5305eb15f13ae3e7975c136592c5e15da8e67dd442797274f30c6399

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 #2,571,934 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
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