Home/Chain Registry/Block #2,114,538

Block #2,114,538

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/13/2017, 5:14:45 PM · Difficulty 10.9003 · 4,726,894 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

373af091f40fcd8c26d21ddd839d7e7dc8234726ffc3395411f4388357f6b29b

View on Chainz ↗

Height

#2,114,538

Difficulty

10.900310

Transactions

Size

2.30 KB

Version

Bits

0ae67abd

Nonce

1,029,611,111

Timestamp

5/13/2017, 5:14:45 PM

Confirmations

4,726,894

Merkle Root

006e133fefa20acc1007dd96cc1f71fc43db07fe68dbd34c16f45eeca30d2602

Transactions (2)

Coinbase19b674db45fdc3…2940b5a6bc444c

1 in → 1 out8.4400 XPM110 B

AKXsVLHd…rQkPiy1C

b626266d8d6f2d…7d610b36d26246

14 in → 2 out212.0000 XPM2.10 KB

AawsTAKP…LkY64ApX AZAUpPRK…y6qkZdaT

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.

2.266 × 10⁹³(94-digit number)

22660100437708874980…06926620809921402880

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

2.266 × 10⁹³(94-digit number)

22660100437708874980…06926620809921402879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.266 × 10⁹³(94-digit number)

22660100437708874980…06926620809921402881

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

4.532 × 10⁹³(94-digit number)

45320200875417749960…13853241619842805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.532 × 10⁹³(94-digit number)

45320200875417749960…13853241619842805761

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

9.064 × 10⁹³(94-digit number)

90640401750835499920…27706483239685611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.064 × 10⁹³(94-digit number)

90640401750835499920…27706483239685611521

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

1.812 × 10⁹⁴(95-digit number)

18128080350167099984…55412966479371223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.812 × 10⁹⁴(95-digit number)

18128080350167099984…55412966479371223041

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

3.625 × 10⁹⁴(95-digit number)

36256160700334199968…10825932958742446079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.625 × 10⁹⁴(95-digit number)

36256160700334199968…10825932958742446081

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 2114538

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 373af091f40fcd8c26d21ddd839d7e7dc8234726ffc3395411f4388357f6b29b

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 #2,114,538 on Chainz ↗

Block #2,114,538

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