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Home/Chain Registry/Block #2,932,969

Block #2,932,969

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/21/2018, 12:50:39 PM Β· Difficulty 11.3972 Β· 3,898,960 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ae45e22a7bdc6dce7aa7dc0af8f67a83bf36e5483e23aa745a1adbdf544fef6
View on Chainz β†—

Difficulty

11.397241

Transactions

1

Size

201 B

Version

2

Bits

0b65b19e

Nonce

913,468,212

Timestamp

11/21/2018, 12:50:39 PM

Confirmations

3,898,960

Merkle Root

0d35d7496b8a90445421a627363972608c7b7ec9719396bd52a2314bef171884
Transactions (1)
Coinbase0d35d7496b8a90…a2314bef171884
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
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.

1.213 Γ— 10⁹⁷(98-digit number)
12134940678716720858…11378545396994048000
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
1.213 Γ— 10⁹⁷(98-digit number)
12134940678716720858…11378545396994047999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.213 Γ— 10⁹⁷(98-digit number)
12134940678716720858…11378545396994048001
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
2.426 Γ— 10⁹⁷(98-digit number)
24269881357433441717…22757090793988095999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.426 Γ— 10⁹⁷(98-digit number)
24269881357433441717…22757090793988096001
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
4.853 Γ— 10⁹⁷(98-digit number)
48539762714866883435…45514181587976191999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.853 Γ— 10⁹⁷(98-digit number)
48539762714866883435…45514181587976192001
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
9.707 Γ— 10⁹⁷(98-digit number)
97079525429733766871…91028363175952383999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.707 Γ— 10⁹⁷(98-digit number)
97079525429733766871…91028363175952384001
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
1.941 Γ— 10⁹⁸(99-digit number)
19415905085946753374…82056726351904767999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.941 Γ— 10⁹⁸(99-digit number)
19415905085946753374…82056726351904768001
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
3.883 Γ— 10⁹⁸(99-digit number)
38831810171893506748…64113452703809535999
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 2932969

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 9ae45e22a7bdc6dce7aa7dc0af8f67a83bf36e5483e23aa745a1adbdf544fef6

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 #2,932,969 on Chainz β†—
Circulating Supply:57,899,549 XPMΒ·at block #6,831,928 Β· updates every 60s
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