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Home/Chain Registry/Block #3,046,821

Block #3,046,821

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/10/2019, 10:14:00 AM Β· Difficulty 10.9961 Β· 3,793,933 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b260cad67dc2a231b17ac8c7555e4844ae1013f96e86f835fae8bbeaeab22857
View on Chainz β†—

Difficulty

10.996091

Transactions

2

Size

1.68 KB

Version

2

Bits

0afeffcc

Nonce

509,049,037

Timestamp

2/10/2019, 10:14:00 AM

Confirmations

3,793,933

Merkle Root

080512f6bc79781dc2a191a4d65e0766209c1480c1bd3c72debb0f0f0ea34154
Transactions (2)
Coinbasef5a43d47b08490…0d8822a6401111
1 in β†’ 1 out8.2900 XPM109 B
AUMQRepm…tAfKmdW1
1ad462e3e9a09d…b97359d4a46aec
10 in β†’ 1 out1985.0882 XPM1.49 KB
ARo9Bx54…mTopc3JB
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.

1.013 Γ— 10⁹³(94-digit number)
10137503239749436519…03750103820297408650
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
1.013 Γ— 10⁹³(94-digit number)
10137503239749436519…03750103820297408649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.013 Γ— 10⁹³(94-digit number)
10137503239749436519…03750103820297408651
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
2.027 Γ— 10⁹³(94-digit number)
20275006479498873039…07500207640594817299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.027 Γ— 10⁹³(94-digit number)
20275006479498873039…07500207640594817301
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
4.055 Γ— 10⁹³(94-digit number)
40550012958997746079…15000415281189634599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.055 Γ— 10⁹³(94-digit number)
40550012958997746079…15000415281189634601
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
8.110 Γ— 10⁹³(94-digit number)
81100025917995492158…30000830562379269199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.110 Γ— 10⁹³(94-digit number)
81100025917995492158…30000830562379269201
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
1.622 Γ— 10⁹⁴(95-digit number)
16220005183599098431…60001661124758538399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.622 Γ— 10⁹⁴(95-digit number)
16220005183599098431…60001661124758538401
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
3.244 Γ— 10⁹⁴(95-digit number)
32440010367198196863…20003322249517076799
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 3046821

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 b260cad67dc2a231b17ac8c7555e4844ae1013f96e86f835fae8bbeaeab22857

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 #3,046,821 on Chainz β†—
Circulating Supply:57,970,374 XPMΒ·at block #6,840,753 Β· updates every 60s
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