Home/Chain Registry/Block #143,858

Block #143,858

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/31/2013, 11:22:13 PM · Difficulty 9.8365 · 6,701,142 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76aeaa2715da1f84c0c2b101747f94f2a38f9080489f9385623065f3ef79e50f

View on Chainz ↗

Height

#143,858

Difficulty

9.836484

Transactions

Size

1005 B

Version

Bits

09d623ca

Nonce

167,319

Timestamp

8/31/2013, 11:22:13 PM

Confirmations

6,701,142

Merkle Root

64c34aab3f92d797af43a149d85da1bbfbb07f717498d5582d15b04bd84010ed

Transactions (2)

Coinbasef37b7a4ec1a4c7…ae605f00f43ea3

1 in → 1 out10.3300 XPM100 B

AbGkvdxH…oihMdBXd

927e29a2bac137…86c51ced07c165

5 in → 2 out152.0023 XPM816 B

AUy92Lrw…bJWnNFg1 AWRzxbGx…ju7z6hhD

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.

9.727 × 10⁹⁰(91-digit number)

97272812743862726306…44567466269575476100

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

9.727 × 10⁹⁰(91-digit number)

97272812743862726306…44567466269575476099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.727 × 10⁹⁰(91-digit number)

97272812743862726306…44567466269575476101

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

1.945 × 10⁹¹(92-digit number)

19454562548772545261…89134932539150952199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.945 × 10⁹¹(92-digit number)

19454562548772545261…89134932539150952201

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

3.890 × 10⁹¹(92-digit number)

38909125097545090522…78269865078301904399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.890 × 10⁹¹(92-digit number)

38909125097545090522…78269865078301904401

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

7.781 × 10⁹¹(92-digit number)

77818250195090181045…56539730156603808799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.781 × 10⁹¹(92-digit number)

77818250195090181045…56539730156603808801

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

1.556 × 10⁹²(93-digit number)

15563650039018036209…13079460313207617599

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 143858

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 76aeaa2715da1f84c0c2b101747f94f2a38f9080489f9385623065f3ef79e50f

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 #143,858 on Chainz ↗

Block #143,858

Cookie Preferences