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Block #2,278,606

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/2/2017, 2:30:59 AM · Difficulty 10.9556 · 4,566,154 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96a296512922665b1bb4289dbcf05d66ea1b0afc06f4a8c461968dfb75d2ff5f

View on Chainz ↗

Height

#2,278,606

Difficulty

10.955576

Transactions

Size

1.53 KB

Version

Bits

0af4a099

Nonce

1,376,445

Timestamp

9/2/2017, 2:30:59 AM

Confirmations

4,566,154

Merkle Root

216a44dd462c876df25bd2b999a47b6083624977e4c7199c45f70644e4d4f4f2

Transactions (4)

Coinbase11e0da4f6ddccb…3ef389040e740b

1 in → 1 out8.3500 XPM109 B

AXDH2a2A…ARWLqu9p

b676d3fad77dc3…b24eabb178b02c

1 in → 2 out3645.6189 XPM226 B

AYDozUuW…bE8mz4Vt AVmoJz1r…1YfwF8HS

2a0bce71ec19ce…5ee519201657ae

7 in → 2 out50.1911 XPM910 B

ARezZb4y…FxP7ivbi AMGfe28J…jfFpbZpk

ce7bb8f759bf59…294c57a665c389

1 in → 2 out4.9093 XPM227 B

AV5bDXsF…JGKHA1dB ARGaPcKm…qx7FvhFm

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.

1.221 × 10⁹⁵(96-digit number)

12211324649199650781…94895384425459040000

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

1.221 × 10⁹⁵(96-digit number)

12211324649199650781…94895384425459039999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.221 × 10⁹⁵(96-digit number)

12211324649199650781…94895384425459040001

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

2.442 × 10⁹⁵(96-digit number)

24422649298399301562…89790768850918079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.442 × 10⁹⁵(96-digit number)

24422649298399301562…89790768850918080001

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

4.884 × 10⁹⁵(96-digit number)

48845298596798603125…79581537701836159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.884 × 10⁹⁵(96-digit number)

48845298596798603125…79581537701836160001

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

9.769 × 10⁹⁵(96-digit number)

97690597193597206250…59163075403672319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.769 × 10⁹⁵(96-digit number)

97690597193597206250…59163075403672320001

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

1.953 × 10⁹⁶(97-digit number)

19538119438719441250…18326150807344639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.953 × 10⁹⁶(97-digit number)

19538119438719441250…18326150807344640001

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 2278606

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 96a296512922665b1bb4289dbcf05d66ea1b0afc06f4a8c461968dfb75d2ff5f

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 #2,278,606 on Chainz ↗

Block #2,278,606

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