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Home/Chain Registry/Block #2,795,978

Block #2,795,978

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 8/16/2018, 2:53:44 AM Β· Difficulty 11.6815 Β· 4,047,457 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
077ea1033adc45d50b234afb4443d46c9fe1f0424f92ae76d102b442dfb17ff7
View on Chainz β†—

Difficulty

11.681468

Transactions

1

Size

200 B

Version

2

Bits

0bae74ab

Nonce

1,551,804,414

Timestamp

8/16/2018, 2:53:44 AM

Confirmations

4,047,457

Merkle Root

425bdbe53fe2a880b88229a4a8fc3ebe2e0f11f3fa8d69df5907b163ad323994
Transactions (1)
Coinbase425bdbe53fe2a8…07b163ad323994
1 in β†’ 1 out7.3200 XPM110 B
AHr8qcn3…YvxusXhY
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.

2.459 Γ— 10⁹⁡(96-digit number)
24592525747154677391…70956213749747816640
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
2.459 Γ— 10⁹⁡(96-digit number)
24592525747154677391…70956213749747816639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.459 Γ— 10⁹⁡(96-digit number)
24592525747154677391…70956213749747816641
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
4.918 Γ— 10⁹⁡(96-digit number)
49185051494309354783…41912427499495633279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.918 Γ— 10⁹⁡(96-digit number)
49185051494309354783…41912427499495633281
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
9.837 Γ— 10⁹⁡(96-digit number)
98370102988618709566…83824854998991266559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.837 Γ— 10⁹⁡(96-digit number)
98370102988618709566…83824854998991266561
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
1.967 Γ— 10⁹⁢(97-digit number)
19674020597723741913…67649709997982533119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.967 Γ— 10⁹⁢(97-digit number)
19674020597723741913…67649709997982533121
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
3.934 Γ— 10⁹⁢(97-digit number)
39348041195447483826…35299419995965066239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.934 Γ— 10⁹⁢(97-digit number)
39348041195447483826…35299419995965066241
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
7.869 Γ— 10⁹⁢(97-digit number)
78696082390894967653…70598839991930132479
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
7.869 Γ— 10⁹⁢(97-digit number)
78696082390894967653…70598839991930132481
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 2795978

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 077ea1033adc45d50b234afb4443d46c9fe1f0424f92ae76d102b442dfb17ff7

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 #2,795,978 on Chainz β†—
Circulating Supply:57,991,851 XPMΒ·at block #6,843,434 Β· updates every 60s
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