Home/Chain Registry/Block #3,113,006

Block #3,113,006

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/27/2019, 8:31:57 PM · Difficulty 11.2395 · 3,724,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b1f6714a5b1a3f0207329318f1efbaa99f32f8bf8e78d6ca4ee989ec771d061c

View on Chainz ↗

Height

#3,113,006

Difficulty

11.239469

Transactions

Size

1.16 KB

Version

Bits

0b3d4dde

Nonce

196,765,408

Timestamp

3/27/2019, 8:31:57 PM

Confirmations

3,724,107

Merkle Root

82795230c9cc9bbcb189505bbdba73f8451adc2820370b453240d8a8abb6ba5c

Transactions (4)

Coinbase68cef02f29b6ef…6bab5a87963273

1 in → 1 out7.9300 XPM110 B

AbXwmGxD…4XXYP765

3fb359c8d96ee9…e94cfd59dbb412

2 in → 2 out15.8700 XPM306 B

AVyDjMkm…1ji94eQY Acskkjn1…oQfaavGo

ba6fc458e35101…2d938814aa3da0

2 in → 2 out13.9300 XPM341 B

APVKWthF…PMMxwRoz AWngK1wN…8UPzn6oB

21b76e08eebb5b…be0a62bf549422

2 in → 2 out11.5700 XPM340 B

APVKWthF…PMMxwRoz ATNcpF15…D2hP3Co5

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.

4.337 × 10⁹⁶(97-digit number)

43372241675921898354…08057060209098311680

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

4.337 × 10⁹⁶(97-digit number)

43372241675921898354…08057060209098311679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.337 × 10⁹⁶(97-digit number)

43372241675921898354…08057060209098311681

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

8.674 × 10⁹⁶(97-digit number)

86744483351843796709…16114120418196623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.674 × 10⁹⁶(97-digit number)

86744483351843796709…16114120418196623361

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

1.734 × 10⁹⁷(98-digit number)

17348896670368759341…32228240836393246719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.734 × 10⁹⁷(98-digit number)

17348896670368759341…32228240836393246721

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

3.469 × 10⁹⁷(98-digit number)

34697793340737518683…64456481672786493439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.469 × 10⁹⁷(98-digit number)

34697793340737518683…64456481672786493441

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

6.939 × 10⁹⁷(98-digit number)

69395586681475037367…28912963345572986879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.939 × 10⁹⁷(98-digit number)

69395586681475037367…28912963345572986881

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

1.387 × 10⁹⁸(99-digit number)

13879117336295007473…57825926691145973759

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 3113006

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 b1f6714a5b1a3f0207329318f1efbaa99f32f8bf8e78d6ca4ee989ec771d061c

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 #3,113,006 on Chainz ↗

Block #3,113,006

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