Block #97,492

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/4/2013, 6:09:28 PM · Difficulty 9.3085 · 6,710,477 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9562f1fa19571f517e864b463f0825c250897926256f546bca3c2704ea7ccfa1

View on Chainz ↗

Height

#97,492

Difficulty

9.308473

Transactions

Size

2.36 KB

Version

Bits

094ef80f

Nonce

1,834,721

Timestamp

8/4/2013, 6:09:28 PM

Confirmations

6,710,477

Mined by

⛏️ P2SHAYtWBH85RetPdsVXF2LbMbcdw3FAcB3ZAR

Merkle Root

699fce41fa7d064070367d671025b4ebe0b41378bbadc27418bf7dfa24e8163b

Transactions (5)

Coinbase3ee127f41a07cb…dfda7296175b20

1 in → 1 out11.5600 XPM109 B

AYtWBH85…FAcB3ZAR

f23c3930d91cd2…0a78c930973cd8

5 in → 2 out58.7400 XPM651 B

ALdtiDNv…TWABhseh Aa6ar9oo…dwYjCneU

682bfa2582c7f1…8bde254d2154ef

2 in → 2 out2.0834 XPM374 B

AcGdjuaf…NRzuCszu AWfmohdH…is16m7gG

f8e313bc74fa77…5b30b0e2600666

5 in → 2 out10.9684 XPM822 B

AbRcMdB8…vmaM8MeE AWVVQT2e…vaSxbNk3

67af6a07969250…813033a2d7d943

2 in → 2 out2.2841 XPM374 B

AbFj7aQB…ETxDSYs3 AJFAyM25…55q6REY8

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.

1.810 × 10⁹⁷(98-digit number)

18105360947471406171…08829684810387832299

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

1.810 × 10⁹⁷(98-digit number)

18105360947471406171…08829684810387832299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.810 × 10⁹⁷(98-digit number)

18105360947471406171…08829684810387832301

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

3.621 × 10⁹⁷(98-digit number)

36210721894942812342…17659369620775664599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.621 × 10⁹⁷(98-digit number)

36210721894942812342…17659369620775664601

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

7.242 × 10⁹⁷(98-digit number)

72421443789885624685…35318739241551329199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.242 × 10⁹⁷(98-digit number)

72421443789885624685…35318739241551329201

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

1.448 × 10⁹⁸(99-digit number)

14484288757977124937…70637478483102658399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.448 × 10⁹⁸(99-digit number)

14484288757977124937…70637478483102658401

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

2.896 × 10⁹⁸(99-digit number)

28968577515954249874…41274956966205316799

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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Cross-reference on Chainz Explorer

Block #97,492

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