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Home/Chain Registry/Block #2,730,983

Block #2,730,983

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 7/2/2018, 11:21:36 AM Β· Difficulty 11.6314 Β· 4,109,475 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
72d9939f05148e00d7c4e5e14cdc9e6d6c07354437333443124dab8113d17329
View on Chainz β†—

Difficulty

11.631429

Transactions

1

Size

201 B

Version

2

Bits

0ba1a55a

Nonce

1,185,528,638

Timestamp

7/2/2018, 11:21:36 AM

Confirmations

4,109,475

Merkle Root

18e986341ab905ae551f66facfd20fe8e0255c4f05894795903ce2e65d6def4b
Transactions (1)
Coinbase18e986341ab905…3ce2e65d6def4b
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.934 Γ— 10⁹⁢(97-digit number)
59349514206439420914…86657708736250880000
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
5.934 Γ— 10⁹⁢(97-digit number)
59349514206439420914…86657708736250879999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.934 Γ— 10⁹⁢(97-digit number)
59349514206439420914…86657708736250880001
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
1.186 Γ— 10⁹⁷(98-digit number)
11869902841287884182…73315417472501759999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.186 Γ— 10⁹⁷(98-digit number)
11869902841287884182…73315417472501760001
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
2.373 Γ— 10⁹⁷(98-digit number)
23739805682575768365…46630834945003519999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.373 Γ— 10⁹⁷(98-digit number)
23739805682575768365…46630834945003520001
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
4.747 Γ— 10⁹⁷(98-digit number)
47479611365151536731…93261669890007039999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.747 Γ— 10⁹⁷(98-digit number)
47479611365151536731…93261669890007040001
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
9.495 Γ— 10⁹⁷(98-digit number)
94959222730303073463…86523339780014079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.495 Γ— 10⁹⁷(98-digit number)
94959222730303073463…86523339780014080001
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
1.899 Γ— 10⁹⁸(99-digit number)
18991844546060614692…73046679560028159999
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.899 Γ— 10⁹⁸(99-digit number)
18991844546060614692…73046679560028160001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2730983

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 72d9939f05148e00d7c4e5e14cdc9e6d6c07354437333443124dab8113d17329

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 #2,730,983 on Chainz β†—
Circulating Supply:57,967,994 XPMΒ·at block #6,840,457 Β· updates every 60s
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