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Block #2,041,720

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2017, 6:27:32 AM · Difficulty 10.6700 · 4,791,996 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c755ccfe1c1d17d691e98581f9ff32b815ffd1704119952731abef4fce68df2d

View on Chainz ↗

Height

#2,041,720

Difficulty

10.669966

Transactions

Size

866 B

Version

Bits

0aab82e8

Nonce

1,366,176,334

Timestamp

3/28/2017, 6:27:32 AM

Confirmations

4,791,996

Merkle Root

af2bf47afcd6db6baf9cc9fed44a9cc1f4defc7e2329448e24c790c95e44e2a1

Transactions (2)

Coinbase825c346b7ea692…28ca8320845936

1 in → 1 out8.7800 XPM109 B

ANfxbrid…pPJGxjWC

4112f33631d25e…e2cc571e9b82c6

1 in → 15 out6.5707 XPM667 B

AXXNFpMq…JBts9TPe AcYXF32w…VidamDkz AVZkypQg…n2TKxwAo AbNgE2wK…GyqrSkVs AYunHiKb…duKB8TWW

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.094 × 10⁹³(94-digit number)

90946125743185508567…06484826313421531000

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

9.094 × 10⁹³(94-digit number)

90946125743185508567…06484826313421530999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.094 × 10⁹³(94-digit number)

90946125743185508567…06484826313421531001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.818 × 10⁹⁴(95-digit number)

18189225148637101713…12969652626843061999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.818 × 10⁹⁴(95-digit number)

18189225148637101713…12969652626843062001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.637 × 10⁹⁴(95-digit number)

36378450297274203426…25939305253686123999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.637 × 10⁹⁴(95-digit number)

36378450297274203426…25939305253686124001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.275 × 10⁹⁴(95-digit number)

72756900594548406853…51878610507372247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.275 × 10⁹⁴(95-digit number)

72756900594548406853…51878610507372248001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.455 × 10⁹⁵(96-digit number)

14551380118909681370…03757221014744495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.455 × 10⁹⁵(96-digit number)

14551380118909681370…03757221014744496001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — 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 →

★★☆☆☆

Rarity

UncommonChain length 10

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 2041720

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 c755ccfe1c1d17d691e98581f9ff32b815ffd1704119952731abef4fce68df2d

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 → Debug Window → 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 #2,041,720 on Chainz ↗

Block #2,041,720

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