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Home/Chain Registry/Block #2,725,549

Block #2,725,549

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/28/2018, 6:37:29 PM Β· Difficulty 11.6231 Β· 4,114,026 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0c7424e5234da40374cf8f5b2f73c941a87273c60b3d7d2ee41a39e028de4eea
View on Chainz β†—

Difficulty

11.623070

Transactions

1

Size

201 B

Version

2

Bits

0b9f818c

Nonce

33,226,007

Timestamp

6/28/2018, 6:37:29 PM

Confirmations

4,114,026

Merkle Root

c6b98df66bf868701452c2ade7420c8e9189da040e14d688b4b9c58a94205866
Transactions (1)
Coinbasec6b98df66bf868…b9c58a94205866
1 in β†’ 1 out7.3900 XPM110 B
AXs9i8Zx…vDDtpzkn
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.

1.406 Γ— 10⁹⁢(97-digit number)
14068351872802901230…35582786270337621760
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
1.406 Γ— 10⁹⁢(97-digit number)
14068351872802901230…35582786270337621759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.406 Γ— 10⁹⁢(97-digit number)
14068351872802901230…35582786270337621761
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
2.813 Γ— 10⁹⁢(97-digit number)
28136703745605802461…71165572540675243519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.813 Γ— 10⁹⁢(97-digit number)
28136703745605802461…71165572540675243521
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
5.627 Γ— 10⁹⁢(97-digit number)
56273407491211604923…42331145081350487039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.627 Γ— 10⁹⁢(97-digit number)
56273407491211604923…42331145081350487041
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
1.125 Γ— 10⁹⁷(98-digit number)
11254681498242320984…84662290162700974079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.125 Γ— 10⁹⁷(98-digit number)
11254681498242320984…84662290162700974081
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
2.250 Γ— 10⁹⁷(98-digit number)
22509362996484641969…69324580325401948159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.250 Γ— 10⁹⁷(98-digit number)
22509362996484641969…69324580325401948161
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
4.501 Γ— 10⁹⁷(98-digit number)
45018725992969283938…38649160650803896319
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 2725549

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 0c7424e5234da40374cf8f5b2f73c941a87273c60b3d7d2ee41a39e028de4eea

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 #2,725,549 on Chainz β†—
Circulating Supply:57,960,886 XPMΒ·at block #6,839,574 Β· updates every 60s
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