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Home/Chain Registry/Block #2,719,789

Block #2,719,789

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 6/24/2018, 8:50:27 PM Β· Difficulty 11.6129 Β· 4,121,493 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27582e2770b80a9fe7aa90153c2a58cabdfd0f834dfbd93ca26ebfcb7919fbaf
View on Chainz β†—

Difficulty

11.612852

Transactions

1

Size

200 B

Version

2

Bits

0b9ce3d6

Nonce

169,835,820

Timestamp

6/24/2018, 8:50:27 PM

Confirmations

4,121,493

Merkle Root

d5a86681f489901e7d50418dd20b24547ed9c0236fe9df2cd425556bfa70d098
Transactions (1)
Coinbased5a86681f48990…25556bfa70d098
1 in β†’ 1 out7.4000 XPM110 B
ALuizqG6…fVE9CLPj
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.

4.718 Γ— 10⁹³(94-digit number)
47184692490201094496…04661131719625267200
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
4.718 Γ— 10⁹³(94-digit number)
47184692490201094496…04661131719625267199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.718 Γ— 10⁹³(94-digit number)
47184692490201094496…04661131719625267201
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
9.436 Γ— 10⁹³(94-digit number)
94369384980402188992…09322263439250534399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.436 Γ— 10⁹³(94-digit number)
94369384980402188992…09322263439250534401
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
1.887 Γ— 10⁹⁴(95-digit number)
18873876996080437798…18644526878501068799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.887 Γ— 10⁹⁴(95-digit number)
18873876996080437798…18644526878501068801
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
3.774 Γ— 10⁹⁴(95-digit number)
37747753992160875596…37289053757002137599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.774 Γ— 10⁹⁴(95-digit number)
37747753992160875596…37289053757002137601
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
7.549 Γ— 10⁹⁴(95-digit number)
75495507984321751193…74578107514004275199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.549 Γ— 10⁹⁴(95-digit number)
75495507984321751193…74578107514004275201
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
1.509 Γ— 10⁹⁡(96-digit number)
15099101596864350238…49156215028008550399
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.509 Γ— 10⁹⁡(96-digit number)
15099101596864350238…49156215028008550401
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 2719789

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 27582e2770b80a9fe7aa90153c2a58cabdfd0f834dfbd93ca26ebfcb7919fbaf

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 #2,719,789 on Chainz β†—
Circulating Supply:57,974,621 XPMΒ·at block #6,841,281 Β· updates every 60s
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