Home/Chain Registry/Block #97,950

Block #97,950

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 12:09:36 AM · Difficulty 9.3236 · 6,726,608 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d609bb4279f3aa9476d5238b137a6ed22d64dfbd06e4526d42686728eae248e9

View on Chainz ↗

Height

#97,950

Difficulty

9.323599

Transactions

Size

541 B

Version

Bits

0952d75b

Nonce

350,314

Timestamp

8/5/2013, 12:09:36 AM

Confirmations

6,726,608

Merkle Root

c624e0507b70440eccfc0b5cdad2ca5701687c851e61bef434d8c16ce4883e83

Transactions (2)

Coinbasea42447a4e7de01…4c678a097d2166

1 in → 1 out11.5000 XPM109 B

AWCd5D8d…B4W6Mbxa

f1c5b13bd601b3…6ca3d3ed7a1914

2 in → 2 out12.0900 XPM341 B

AVnqxjPf…DLNmgyZ2 ANPs1qSK…vmGYLi2V

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.

1.565 × 10⁹⁸(99-digit number)

15651651330741539997…77222758965721555200

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

1.565 × 10⁹⁸(99-digit number)

15651651330741539997…77222758965721555199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.565 × 10⁹⁸(99-digit number)

15651651330741539997…77222758965721555201

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

3.130 × 10⁹⁸(99-digit number)

31303302661483079994…54445517931443110399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.130 × 10⁹⁸(99-digit number)

31303302661483079994…54445517931443110401

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

6.260 × 10⁹⁸(99-digit number)

62606605322966159988…08891035862886220799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.260 × 10⁹⁸(99-digit number)

62606605322966159988…08891035862886220801

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

1.252 × 10⁹⁹(100-digit number)

12521321064593231997…17782071725772441599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.252 × 10⁹⁹(100-digit number)

12521321064593231997…17782071725772441601

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

2.504 × 10⁹⁹(100-digit number)

25042642129186463995…35564143451544883199

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 97950

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 d609bb4279f3aa9476d5238b137a6ed22d64dfbd06e4526d42686728eae248e9

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 #97,950 on Chainz ↗

Block #97,950

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