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Block #2,177,213

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2017, 11:04:28 AM · Difficulty 10.9219 · 4,668,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15cca2aadc6be53d20ed1ba0a7d801fd1794922d1cccd8150327307f9b49b838

View on Chainz ↗

Height

#2,177,213

Difficulty

10.921868

Transactions

Size

428 B

Version

Bits

0aebff86

Nonce

17,692,288

Timestamp

6/25/2017, 11:04:28 AM

Confirmations

4,668,434

Merkle Root

36db19be6b3a9342992286da579efe8e8efe3da96decc59b516291c7b2532d03

Transactions (2)

Coinbasee9c80765939672…ca76007404eb25

1 in → 1 out8.3800 XPM110 B

AesGYTr3…iJDGYDwd

815304a7162011…e1371a1db2bc36

1 in → 2 out3222.6900 XPM227 B

AMoJH4oU…ESnXnGVJ APTfFPVp…4R3sQWWv

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.

1.381 × 10⁹⁶(97-digit number)

13810862679292083838…35229818676573089280

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

1.381 × 10⁹⁶(97-digit number)

13810862679292083838…35229818676573089279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.381 × 10⁹⁶(97-digit number)

13810862679292083838…35229818676573089281

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

2.762 × 10⁹⁶(97-digit number)

27621725358584167676…70459637353146178559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.762 × 10⁹⁶(97-digit number)

27621725358584167676…70459637353146178561

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

5.524 × 10⁹⁶(97-digit number)

55243450717168335352…40919274706292357119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.524 × 10⁹⁶(97-digit number)

55243450717168335352…40919274706292357121

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

1.104 × 10⁹⁷(98-digit number)

11048690143433667070…81838549412584714239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.104 × 10⁹⁷(98-digit number)

11048690143433667070…81838549412584714241

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

2.209 × 10⁹⁷(98-digit number)

22097380286867334141…63677098825169428479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.209 × 10⁹⁷(98-digit number)

22097380286867334141…63677098825169428481

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 2177213

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 15cca2aadc6be53d20ed1ba0a7d801fd1794922d1cccd8150327307f9b49b838

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 #2,177,213 on Chainz ↗

Block #2,177,213

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