Home/Chain Registry/Block #3,327,801

Block #3,327,801

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/26/2019, 10:01:54 AM · Difficulty 11.0323 · 3,517,847 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46b94264798ad3976a37be59d100bd6758987e9cd9285cf7919442c5f0eb958c

View on Chainz ↗

Height

#3,327,801

Difficulty

11.032287

Transactions

Size

1.32 KB

Version

Bits

0b0843f4

Nonce

2,125,292,371

Timestamp

8/26/2019, 10:01:54 AM

Confirmations

3,517,847

Merkle Root

eea05c356f4f641aa89f4be8bde080a3fb24109b1b2febce07ef758d0f9ead2d

Transactions (3)

Coinbase50e87a04f68271…4f7be4202fed52

1 in → 1 out8.2300 XPM109 B

ASiq2qtK…VMhmk7yL

3324c46cdbdf67…73b05fee8e6eda

1 in → 2 out8.2000 XPM191 B

ANkkLLes…CEJqMsJZ ASiq2qtK…VMhmk7yL

59ef14ed90adb0…90ac10a2dd3853

6 in → 2 out4.0358 XPM963 B

ASiq2qtK…VMhmk7yL ATEYYXLB…Es56XvRT

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.

4.010 × 10⁹⁷(98-digit number)

40104225688260825650…62414153655556341760

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

4.010 × 10⁹⁷(98-digit number)

40104225688260825650…62414153655556341759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.010 × 10⁹⁷(98-digit number)

40104225688260825650…62414153655556341761

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

8.020 × 10⁹⁷(98-digit number)

80208451376521651300…24828307311112683519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.020 × 10⁹⁷(98-digit number)

80208451376521651300…24828307311112683521

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

1.604 × 10⁹⁸(99-digit number)

16041690275304330260…49656614622225367039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.604 × 10⁹⁸(99-digit number)

16041690275304330260…49656614622225367041

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

3.208 × 10⁹⁸(99-digit number)

32083380550608660520…99313229244450734079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.208 × 10⁹⁸(99-digit number)

32083380550608660520…99313229244450734081

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

6.416 × 10⁹⁸(99-digit number)

64166761101217321040…98626458488901468159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.416 × 10⁹⁸(99-digit number)

64166761101217321040…98626458488901468161

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.283 × 10⁹⁹(100-digit number)

12833352220243464208…97252916977802936319

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 3327801

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 46b94264798ad3976a37be59d100bd6758987e9cd9285cf7919442c5f0eb958c

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 #3,327,801 on Chainz ↗

Block #3,327,801

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