Block #99,973

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 10:47:21 PM · Difficulty 9.4093 · 6,696,829 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

053c912f861b1c62acfe4721cad02b46cb3a527e1b8d6e5bd56b6c7092a97140

View on Chainz ↗

Height

#99,973

Difficulty

9.409330

Transactions

Size

558 B

Version

Bits

0968c9dc

Nonce

376,862

Timestamp

8/5/2013, 10:47:21 PM

Confirmations

6,696,829

Mined by

⛏️ P2SHAHtDFTRkEftfVoxmBKZjY3X5QzB13BPGag

Merkle Root

1606bf4fb3bb17040a80641a57c0d2d16e8a7d099655cc448b9474c33afac998

Transactions (3)

Coinbase01e1e822467fa2…a9558e374d12dc

1 in → 1 out11.3000 XPM109 B

AHtDFTRk…B13BPGag

57bbe7e3fcf5da…ab4a71d13b73df

1 in → 2 out11.6300 XPM192 B

AdwGP6Fz…PchFe13M AHF7D97A…zwSniWTS

0d0927e15100a9…18efdc5bf24f08

1 in → 1 out11.6000 XPM158 B

AYQgZje2…fn4pgV5R

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.

7.211 × 10¹¹⁶(117-digit number)

72111437328578197207…23075636133288010239

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

7.211 × 10¹¹⁶(117-digit number)

72111437328578197207…23075636133288010239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.211 × 10¹¹⁶(117-digit number)

72111437328578197207…23075636133288010241

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

1.442 × 10¹¹⁷(118-digit number)

14422287465715639441…46151272266576020479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.442 × 10¹¹⁷(118-digit number)

14422287465715639441…46151272266576020481

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

2.884 × 10¹¹⁷(118-digit number)

28844574931431278883…92302544533152040959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.884 × 10¹¹⁷(118-digit number)

28844574931431278883…92302544533152040961

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

5.768 × 10¹¹⁷(118-digit number)

57689149862862557766…84605089066304081919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.768 × 10¹¹⁷(118-digit number)

57689149862862557766…84605089066304081921

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

1.153 × 10¹¹⁸(119-digit number)

11537829972572511553…69210178132608163839

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