Home/Chain Registry/Block #3,062,574

Block #3,062,574

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/21/2019, 12:28:53 PM · Difficulty 11.0078 · 3,779,259 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dedf5296dace7206a3dd63dc8cf75abbbd7ee9e9c9c2541df86ea183cfc502f8

View on Chainz ↗

Height

#3,062,574

Difficulty

11.007826

Transactions

Size

765 B

Version

Bits

0b0200e1

Nonce

94,732,426

Timestamp

2/21/2019, 12:28:53 PM

Confirmations

3,779,259

Merkle Root

e1958f95db6a9e5580b29db69628721dd2f1d622d3f29137df0ff4967d09d6b8

Transactions (3)

Coinbase6a173858b31a80…d1f7ed8c33acc5

1 in → 1 out8.2600 XPM109 B

AUMQRepm…tAfKmdW1

ef320f59d10d4e…3ea3b1addebf38

2 in → 2 out11.3942 XPM339 B

AZtM1QsL…JugreUPy AbXwmGxD…4XXYP765

6e95126e917241…bf853657a84ca1

1 in → 2 out1.7979 XPM227 B

AbXwmGxD…4XXYP765 AP21FpxC…ntAWgp39

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.

9.406 × 10⁹⁴(95-digit number)

94062097808893967842…85087319067387883200

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

9.406 × 10⁹⁴(95-digit number)

94062097808893967842…85087319067387883199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.406 × 10⁹⁴(95-digit number)

94062097808893967842…85087319067387883201

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

1.881 × 10⁹⁵(96-digit number)

18812419561778793568…70174638134775766399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.881 × 10⁹⁵(96-digit number)

18812419561778793568…70174638134775766401

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

3.762 × 10⁹⁵(96-digit number)

37624839123557587137…40349276269551532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.762 × 10⁹⁵(96-digit number)

37624839123557587137…40349276269551532801

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

7.524 × 10⁹⁵(96-digit number)

75249678247115174274…80698552539103065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.524 × 10⁹⁵(96-digit number)

75249678247115174274…80698552539103065601

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

1.504 × 10⁹⁶(97-digit number)

15049935649423034854…61397105078206131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.504 × 10⁹⁶(97-digit number)

15049935649423034854…61397105078206131201

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

3.009 × 10⁹⁶(97-digit number)

30099871298846069709…22794210156412262399

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 3062574

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 dedf5296dace7206a3dd63dc8cf75abbbd7ee9e9c9c2541df86ea183cfc502f8

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 #3,062,574 on Chainz ↗

Block #3,062,574

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