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Block #2,213,078

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/19/2017, 6:44:48 AM · Difficulty 10.9439 · 4,630,935 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6697d638a2ce3fe11fb2e41ea594b6eda1e86e652c8a1de96a4999f02df5159c

View on Chainz ↗

Height

#2,213,078

Difficulty

10.943870

Transactions

Size

1.07 KB

Version

Bits

0af1a17a

Nonce

993,495,962

Timestamp

7/19/2017, 6:44:48 AM

Confirmations

4,630,935

Merkle Root

dc1f86d5bf13f20a293b26e1d3044f789d7cca7324f7c74616ed467c91222977

Transactions (3)

Coinbase7e0161c55f9784…d405eb1834d087

1 in → 1 out8.3600 XPM110 B

AbPdSZ1S…jbxLUtPD

d874bd87cb2a7b…b3a0499cfbdf2e

4 in → 2 out6794.5060 XPM671 B

Ada1dx2w…8gd1gZg2 ALAWFYjG…oYztPCoW

259298f179e02c…76705e727eb34b

1 in → 2 out103.8361 XPM226 B

AbXNreUG…7Nm8xDUY AXZRPQrh…sJnGwMTb

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.

1.169 × 10⁹⁶(97-digit number)

11693304918595631246…20602298627231582720

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

1.169 × 10⁹⁶(97-digit number)

11693304918595631246…20602298627231582719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.169 × 10⁹⁶(97-digit number)

11693304918595631246…20602298627231582721

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

2.338 × 10⁹⁶(97-digit number)

23386609837191262492…41204597254463165439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.338 × 10⁹⁶(97-digit number)

23386609837191262492…41204597254463165441

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

4.677 × 10⁹⁶(97-digit number)

46773219674382524985…82409194508926330879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.677 × 10⁹⁶(97-digit number)

46773219674382524985…82409194508926330881

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

9.354 × 10⁹⁶(97-digit number)

93546439348765049971…64818389017852661759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.354 × 10⁹⁶(97-digit number)

93546439348765049971…64818389017852661761

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

1.870 × 10⁹⁷(98-digit number)

18709287869753009994…29636778035705323519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.870 × 10⁹⁷(98-digit number)

18709287869753009994…29636778035705323521

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 2213078

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 6697d638a2ce3fe11fb2e41ea594b6eda1e86e652c8a1de96a4999f02df5159c

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 #2,213,078 on Chainz ↗

Block #2,213,078

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