Home/Chain Registry/Block #270,157

Block #270,157

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 6:06:10 PM · Difficulty 9.9518 · 6,570,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28c9f5913d2a4546bf770aa3d933c648615101b40b0ade7478a5dcfc97aad9c1

View on Chainz ↗

Height

#270,157

Difficulty

9.951788

Transactions

Size

1.43 KB

Version

Bits

09f3a85d

Nonce

19,675

Timestamp

11/23/2013, 6:06:10 PM

Confirmations

6,570,643

Merkle Root

89ff516a93c0a056139c0ec0d27627bdf5ac816694fb38b7507560c1c26c597c

Transactions (2)

Coinbase24a945d7d232a1…fb672cc06fec2c

1 in → 1 out10.1000 XPM109 B

AJDmcvFu…h5ihYYvY

749817b2317276…a60bead971f8ee

8 in → 2 out61.0407 XPM1.24 KB

ANNoPW8X…otPpgKrN AZK22v27…kXFYmAM4

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.

1.446 × 10⁸⁹(90-digit number)

14465432455177441330…01801553753776246400

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

1.446 × 10⁸⁹(90-digit number)

14465432455177441330…01801553753776246399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.446 × 10⁸⁹(90-digit number)

14465432455177441330…01801553753776246401

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

2.893 × 10⁸⁹(90-digit number)

28930864910354882661…03603107507552492799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.893 × 10⁸⁹(90-digit number)

28930864910354882661…03603107507552492801

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

5.786 × 10⁸⁹(90-digit number)

57861729820709765322…07206215015104985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.786 × 10⁸⁹(90-digit number)

57861729820709765322…07206215015104985601

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

1.157 × 10⁹⁰(91-digit number)

11572345964141953064…14412430030209971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.157 × 10⁹⁰(91-digit number)

11572345964141953064…14412430030209971201

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

2.314 × 10⁹⁰(91-digit number)

23144691928283906128…28824860060419942399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 270157

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 28c9f5913d2a4546bf770aa3d933c648615101b40b0ade7478a5dcfc97aad9c1

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 #270,157 on Chainz ↗

Block #270,157

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