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Home/Chain Registry/Block #2,782,995

Block #2,782,995

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2018, 7:43:20 AM Β· Difficulty 11.6606 Β· 4,059,517 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
84d66bbc60309a978e449bbb7d79ce23cba6c4e7da2a7f05e2c3e422d6e524e9
View on Chainz β†—

Difficulty

11.660647

Transactions

2

Size

1.71 KB

Version

2

Bits

0ba92029

Nonce

573,543,548

Timestamp

8/7/2018, 7:43:20 AM

Confirmations

4,059,517

Merkle Root

547d9360564b9351f8397b98fe00a9b6840f1d81ba4479734875ccfb28b31103
Transactions (2)
Coinbase2d2e37e115f57d…0fdfe2e7ecee8a
1 in β†’ 1 out7.3600 XPM109 B
AJMwM6jp…wzeS7tJs
e3bfcdd6cc7937…32728e9c1a2d56
10 in β†’ 2 out39.9800 XPM1.52 KB
AGLHtz2B…AssoJuj5AGuEFTnh…SktbZx7R
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.

1.477 Γ— 10⁹³(94-digit number)
14779798201975114800…37264109960644764600
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
1.477 Γ— 10⁹³(94-digit number)
14779798201975114800…37264109960644764599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.477 Γ— 10⁹³(94-digit number)
14779798201975114800…37264109960644764601
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
2.955 Γ— 10⁹³(94-digit number)
29559596403950229601…74528219921289529199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.955 Γ— 10⁹³(94-digit number)
29559596403950229601…74528219921289529201
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
5.911 Γ— 10⁹³(94-digit number)
59119192807900459203…49056439842579058399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.911 Γ— 10⁹³(94-digit number)
59119192807900459203…49056439842579058401
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
1.182 Γ— 10⁹⁴(95-digit number)
11823838561580091840…98112879685158116799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.182 Γ— 10⁹⁴(95-digit number)
11823838561580091840…98112879685158116801
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
2.364 Γ— 10⁹⁴(95-digit number)
23647677123160183681…96225759370316233599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.364 Γ— 10⁹⁴(95-digit number)
23647677123160183681…96225759370316233601
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
4.729 Γ— 10⁹⁴(95-digit number)
47295354246320367362…92451518740632467199
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 2782995

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 84d66bbc60309a978e449bbb7d79ce23cba6c4e7da2a7f05e2c3e422d6e524e9

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 #2,782,995 on Chainz β†—
Circulating Supply:57,984,515 XPMΒ·at block #6,842,511 Β· updates every 60s
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