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Home/Chain Registry/Block #2,726,218

Block #2,726,218

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/29/2018, 5:28:14 AM Β· Difficulty 11.6245 Β· 4,119,148 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8444a5ba347c5f653eda499dc53d056d02e13ccd6171bbcbdbc95dfd828c57b5
View on Chainz β†—

Difficulty

11.624463

Transactions

1

Size

199 B

Version

2

Bits

0b9fdcd0

Nonce

1,441,811,648

Timestamp

6/29/2018, 5:28:14 AM

Confirmations

4,119,148

Merkle Root

c75a4cc65f64e8c13666314e8c27594570086bca5a887f025bea7f3feb28e5ce
Transactions (1)
Coinbasec75a4cc65f64e8…ea7f3feb28e5ce
1 in β†’ 1 out7.3900 XPM110 B
ATU8ydaD…o94zg4uv
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.

1.971 Γ— 10⁹³(94-digit number)
19710761056240850921…65847298605250556480
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
1.971 Γ— 10⁹³(94-digit number)
19710761056240850921…65847298605250556479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.971 Γ— 10⁹³(94-digit number)
19710761056240850921…65847298605250556481
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
3.942 Γ— 10⁹³(94-digit number)
39421522112481701843…31694597210501112959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.942 Γ— 10⁹³(94-digit number)
39421522112481701843…31694597210501112961
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
7.884 Γ— 10⁹³(94-digit number)
78843044224963403687…63389194421002225919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.884 Γ— 10⁹³(94-digit number)
78843044224963403687…63389194421002225921
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
1.576 Γ— 10⁹⁴(95-digit number)
15768608844992680737…26778388842004451839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.576 Γ— 10⁹⁴(95-digit number)
15768608844992680737…26778388842004451841
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
3.153 Γ— 10⁹⁴(95-digit number)
31537217689985361474…53556777684008903679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.153 Γ— 10⁹⁴(95-digit number)
31537217689985361474…53556777684008903681
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
6.307 Γ— 10⁹⁴(95-digit number)
63074435379970722949…07113555368017807359
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 2726218

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 8444a5ba347c5f653eda499dc53d056d02e13ccd6171bbcbdbc95dfd828c57b5

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 #2,726,218 on Chainz β†—
Circulating Supply:58,007,373 XPMΒ·at block #6,845,365 Β· updates every 60s
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