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Home/Chain Registry/Block #2,551,740

Block #2,551,740

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/6/2018, 11:20:54 AM Β· Difficulty 10.9894 Β· 4,273,783 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8b2565c2df62b06b8a44c0dfadcb791b8abeec793cee972251a8f83a1d3fae9f
View on Chainz β†—

Difficulty

10.989431

Transactions

1

Size

199 B

Version

2

Bits

0afd4b5c

Nonce

656,676,514

Timestamp

3/6/2018, 11:20:54 AM

Confirmations

4,273,783

Merkle Root

5144f553164a51f82b29873bab1a2a4985cf0a3a333957484ad2da1d86e775eb
Transactions (1)
Coinbase5144f553164a51…d2da1d86e775eb
1 in β†’ 1 out8.2700 XPM109 B
ALQGpaT6…9dLVU1B9
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.

1.861 Γ— 10⁹⁡(96-digit number)
18613347950990670510…47822564159239259520
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
1.861 Γ— 10⁹⁡(96-digit number)
18613347950990670510…47822564159239259519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.861 Γ— 10⁹⁡(96-digit number)
18613347950990670510…47822564159239259521
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
3.722 Γ— 10⁹⁡(96-digit number)
37226695901981341020…95645128318478519039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.722 Γ— 10⁹⁡(96-digit number)
37226695901981341020…95645128318478519041
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
7.445 Γ— 10⁹⁡(96-digit number)
74453391803962682040…91290256636957038079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.445 Γ— 10⁹⁡(96-digit number)
74453391803962682040…91290256636957038081
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
1.489 Γ— 10⁹⁢(97-digit number)
14890678360792536408…82580513273914076159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.489 Γ— 10⁹⁢(97-digit number)
14890678360792536408…82580513273914076161
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
2.978 Γ— 10⁹⁢(97-digit number)
29781356721585072816…65161026547828152319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.978 Γ— 10⁹⁢(97-digit number)
29781356721585072816…65161026547828152321
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
5.956 Γ— 10⁹⁢(97-digit number)
59562713443170145632…30322053095656304639
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 2551740

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 8b2565c2df62b06b8a44c0dfadcb791b8abeec793cee972251a8f83a1d3fae9f

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 #2,551,740 on Chainz β†—
Circulating Supply:57,848,280 XPMΒ·at block #6,825,522 Β· updates every 60s
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