Home/Chain Registry/Block #88,212

Block #88,212

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 11:18:48 AM · Difficulty 9.2699 · 6,707,076 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7435c5d69b630f03c61d74edc09e6499600862f4f22fc3d0ec4852c88c0dedfa

View on Chainz ↗

Height

#88,212

Difficulty

9.269913

Transactions

Size

892 B

Version

Bits

0945190a

Nonce

124,512

Timestamp

7/29/2013, 11:18:48 AM

Confirmations

6,707,076

Merkle Root

0341e8482a954d59da7449f9f682eb4dfafa7375f14b859023a055615d8a0cdb

Transactions (3)

Coinbase5da7f501b80d72…471bc9f8397083

1 in → 1 out11.6400 XPM109 B

AULVBi1Q…SrbkC2hb

a46f3adecf7a28…98b9a9986d3a9a

4 in → 1 out54.8200 XPM534 B

AbJ7AHBK…A7y4jMpk

db5daa332acff4…3d39932f6a453f

1 in → 1 out11.5900 XPM157 B

AcjRZamd…XfNvPJsT

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.

1.400 × 10¹⁰⁰(101-digit number)

14002354902546819858…44846250129267305400

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

1.400 × 10¹⁰⁰(101-digit number)

14002354902546819858…44846250129267305399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.400 × 10¹⁰⁰(101-digit number)

14002354902546819858…44846250129267305401

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

2.800 × 10¹⁰⁰(101-digit number)

28004709805093639716…89692500258534610799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.800 × 10¹⁰⁰(101-digit number)

28004709805093639716…89692500258534610801

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

5.600 × 10¹⁰⁰(101-digit number)

56009419610187279433…79385000517069221599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.600 × 10¹⁰⁰(101-digit number)

56009419610187279433…79385000517069221601

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

1.120 × 10¹⁰¹(102-digit number)

11201883922037455886…58770001034138443199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.120 × 10¹⁰¹(102-digit number)

11201883922037455886…58770001034138443201

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

2.240 × 10¹⁰¹(102-digit number)

22403767844074911773…17540002068276886399

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 88212

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 7435c5d69b630f03c61d74edc09e6499600862f4f22fc3d0ec4852c88c0dedfa

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 #88,212 on Chainz ↗