Home/Chain Registry/Block #103,090

Block #103,090

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/7/2013, 10:32:59 AM · Difficulty 9.5150 · 6,721,940 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8de46acf82b3848f210399999837aab2d408282de883819f17d6e9b4e82a09c1

View on Chainz ↗

Height

#103,090

Difficulty

9.515027

Transactions

Size

872 B

Version

Bits

0983d8c8

Nonce

25,760

Timestamp

8/7/2013, 10:32:59 AM

Confirmations

6,721,940

Merkle Root

ea68b8330b2a9176df8c99a86394e874b8f84dfa0cad77c3446809e535411e37

Transactions (2)

Coinbase3f359df9f3018c…d06be25162113d

1 in → 1 out11.0400 XPM109 B

AFoUf1rp…xfPLEged

9ad1a509ef8916…666c1d79205d46

4 in → 2 out1660.0101 XPM672 B

ASRgGwHH…DGU87Qq4 AYbQAeeg…c6b1V1sS

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.

1.140 × 10⁹⁷(98-digit number)

11400523691570803462…90968875623329001600

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

1.140 × 10⁹⁷(98-digit number)

11400523691570803462…90968875623329001599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.140 × 10⁹⁷(98-digit number)

11400523691570803462…90968875623329001601

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

2.280 × 10⁹⁷(98-digit number)

22801047383141606924…81937751246658003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.280 × 10⁹⁷(98-digit number)

22801047383141606924…81937751246658003201

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

4.560 × 10⁹⁷(98-digit number)

45602094766283213849…63875502493316006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.560 × 10⁹⁷(98-digit number)

45602094766283213849…63875502493316006401

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

9.120 × 10⁹⁷(98-digit number)

91204189532566427699…27751004986632012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.120 × 10⁹⁷(98-digit number)

91204189532566427699…27751004986632012801

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

1.824 × 10⁹⁸(99-digit number)

18240837906513285539…55502009973264025599

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 103090

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 8de46acf82b3848f210399999837aab2d408282de883819f17d6e9b4e82a09c1

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 #103,090 on Chainz ↗

Block #103,090

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