Block #97,779

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/4/2013, 9:51:43 PM · Difficulty 9.3187 · 6,709,578 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2488e3b1381153eac8fe4035c1f44ac65358124914032761e6c9e1925686e5eb

View on Chainz ↗

Height

#97,779

Difficulty

9.318675

Transactions

Size

358 B

Version

Bits

095194a9

Nonce

618,897

Timestamp

8/4/2013, 9:51:43 PM

Confirmations

6,709,578

Mined by

⛏️ P2SHATgawmkS5VKh3GyMpBttrPgLqJTAkDGCZc

Merkle Root

faaf0317ade0c392fbf1f2a3c446b000f7e1e74504326523204fb1e902a3e80f

Transactions (2)

Coinbase50c3b3edd09283…ccc1654040192d

1 in → 1 out11.5100 XPM109 B

ATgawmkS…TAkDGCZc

b3410255316327…fe0872e6e18950

1 in → 1 out11.8000 XPM158 B

Ad91bTac…3L6H7xaC

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.

2.338 × 10⁹⁶(97-digit number)

23382588099845835902…85414701375752596009

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

2.338 × 10⁹⁶(97-digit number)

23382588099845835902…85414701375752596009

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.338 × 10⁹⁶(97-digit number)

23382588099845835902…85414701375752596011

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

4.676 × 10⁹⁶(97-digit number)

46765176199691671805…70829402751505192019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.676 × 10⁹⁶(97-digit number)

46765176199691671805…70829402751505192021

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

9.353 × 10⁹⁶(97-digit number)

93530352399383343610…41658805503010384039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.353 × 10⁹⁶(97-digit number)

93530352399383343610…41658805503010384041

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

1.870 × 10⁹⁷(98-digit number)

18706070479876668722…83317611006020768079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.870 × 10⁹⁷(98-digit number)

18706070479876668722…83317611006020768081

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

3.741 × 10⁹⁷(98-digit number)

37412140959753337444…66635222012041536159

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 #97,779

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