Home/Chain Registry/Block #154,264

Block #154,264

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/7/2013, 1:16:34 PM · Difficulty 9.8645 · 6,671,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbbd9328bc0db71f047c9151cea8c72185bcbc118c0d3211fe80ed2913edf545

View on Chainz ↗

Height

#154,264

Difficulty

9.864523

Transactions

Size

470 B

Version

Bits

09dd515e

Nonce

48,146

Timestamp

9/7/2013, 1:16:34 PM

Confirmations

6,671,361

Merkle Root

328134d7fd713d71996d51508d9e990c0f5a7c4af7ff8f84037c847ad4bcbc8b

Transactions (2)

Coinbase688591b2ed2d0a…83c18eff7bd6e8

1 in → 1 out10.2700 XPM109 B

AQNswXCw…VPJfwdMA

4a97d4a19f9d3e…2c24578fe1e0a0

2 in → 1 out20.8500 XPM272 B

Abvzzvcw…XeyEZ1PD

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.

7.052 × 10⁹²(93-digit number)

70522157964759810370…12884147482819346780

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

7.052 × 10⁹²(93-digit number)

70522157964759810370…12884147482819346779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.052 × 10⁹²(93-digit number)

70522157964759810370…12884147482819346781

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

1.410 × 10⁹³(94-digit number)

14104431592951962074…25768294965638693559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.410 × 10⁹³(94-digit number)

14104431592951962074…25768294965638693561

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

2.820 × 10⁹³(94-digit number)

28208863185903924148…51536589931277387119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.820 × 10⁹³(94-digit number)

28208863185903924148…51536589931277387121

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

5.641 × 10⁹³(94-digit number)

56417726371807848296…03073179862554774239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.641 × 10⁹³(94-digit number)

56417726371807848296…03073179862554774241

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

1.128 × 10⁹⁴(95-digit number)

11283545274361569659…06146359725109548479

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 154264

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 bbbd9328bc0db71f047c9151cea8c72185bcbc118c0d3211fe80ed2913edf545

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 #154,264 on Chainz ↗

Block #154,264

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