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Home/Chain Registry/Block #3,030,488

Block #3,030,488

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/29/2019, 3:29:11 PM Β· Difficulty 11.1086 Β· 3,796,115 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2987eb73c9a0ef53f67341b2fc8794043a7e5a625338f5ee80a2cd957a1e5d63
View on Chainz β†—

Difficulty

11.108629

Transactions

1

Size

201 B

Version

2

Bits

0b1bcf15

Nonce

333,364,517

Timestamp

1/29/2019, 3:29:11 PM

Confirmations

3,796,115

Merkle Root

b577092f29b3c9f3c5686bb5439ca8f81747ada03d43dd0e729e8a68a2b94996
Transactions (1)
Coinbaseb577092f29b3c9…9e8a68a2b94996
1 in β†’ 1 out8.0900 XPM109 B
AUhjokok…k5m93PZR
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.

2.572 Γ— 10⁹⁸(99-digit number)
25729847954328861940…29001375640304783360
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
2.572 Γ— 10⁹⁸(99-digit number)
25729847954328861940…29001375640304783359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.572 Γ— 10⁹⁸(99-digit number)
25729847954328861940…29001375640304783361
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
5.145 Γ— 10⁹⁸(99-digit number)
51459695908657723881…58002751280609566719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.145 Γ— 10⁹⁸(99-digit number)
51459695908657723881…58002751280609566721
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
1.029 Γ— 10⁹⁹(100-digit number)
10291939181731544776…16005502561219133439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.029 Γ— 10⁹⁹(100-digit number)
10291939181731544776…16005502561219133441
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
2.058 Γ— 10⁹⁹(100-digit number)
20583878363463089552…32011005122438266879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.058 Γ— 10⁹⁹(100-digit number)
20583878363463089552…32011005122438266881
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
4.116 Γ— 10⁹⁹(100-digit number)
41167756726926179105…64022010244876533759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.116 Γ— 10⁹⁹(100-digit number)
41167756726926179105…64022010244876533761
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
8.233 Γ— 10⁹⁹(100-digit number)
82335513453852358210…28044020489753067519
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 3030488

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 2987eb73c9a0ef53f67341b2fc8794043a7e5a625338f5ee80a2cd957a1e5d63

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 #3,030,488 on Chainz β†—
Circulating Supply:57,856,976 XPMΒ·at block #6,826,602 Β· updates every 60s
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