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Home/Chain Registry/Block #2,782,719

Block #2,782,719

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2018, 3:45:46 AM Β· Difficulty 11.6581 Β· 4,062,560 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
64d861c31aeb9e2c997dedac18f2ff644e77bdd4f293cec93ce350108fbadb53
View on Chainz β†—

Difficulty

11.658061

Transactions

1

Size

199 B

Version

2

Bits

0ba876b5

Nonce

273,694,734

Timestamp

8/7/2018, 3:45:46 AM

Confirmations

4,062,560

Merkle Root

2a098db64f156e08ac040884ce9bfa85630c9d3e70ca2ef6efc09678945d094a
Transactions (1)
Coinbase2a098db64f156e…c09678945d094a
1 in β†’ 1 out7.3500 XPM110 B
Aao9YhSc…wrrACnFR
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.

8.741 Γ— 10⁹¹(92-digit number)
87419194495987392091…59027493915925084540
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
8.741 Γ— 10⁹¹(92-digit number)
87419194495987392091…59027493915925084539
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.741 Γ— 10⁹¹(92-digit number)
87419194495987392091…59027493915925084541
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
1.748 Γ— 10⁹²(93-digit number)
17483838899197478418…18054987831850169079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.748 Γ— 10⁹²(93-digit number)
17483838899197478418…18054987831850169081
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
3.496 Γ— 10⁹²(93-digit number)
34967677798394956836…36109975663700338159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.496 Γ— 10⁹²(93-digit number)
34967677798394956836…36109975663700338161
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
6.993 Γ— 10⁹²(93-digit number)
69935355596789913673…72219951327400676319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.993 Γ— 10⁹²(93-digit number)
69935355596789913673…72219951327400676321
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
1.398 Γ— 10⁹³(94-digit number)
13987071119357982734…44439902654801352639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.398 Γ— 10⁹³(94-digit number)
13987071119357982734…44439902654801352641
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
2.797 Γ— 10⁹³(94-digit number)
27974142238715965469…88879805309602705279
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 2782719

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 64d861c31aeb9e2c997dedac18f2ff644e77bdd4f293cec93ce350108fbadb53

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 #2,782,719 on Chainz β†—
Circulating Supply:58,006,667 XPMΒ·at block #6,845,278 Β· updates every 60s
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