Block #121,944

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 4:02:48 AM · Difficulty 9.7541 · 6,704,894 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff2d0e1924d6386aa643815ec6ddbdbf56ebbd759394fb0784fba12648658121

View on Chainz ↗

Height

#121,944

Difficulty

9.754130

Transactions

Size

935 B

Version

Bits

09c10ea4

Nonce

402,229

Timestamp

8/18/2013, 4:02:48 AM

Confirmations

6,704,894

Mined by

⛏️ P2SHAPksWEGUnFhTLphnyPHFaGXcYR6iViiT8T

Merkle Root

106a03e81235a6a618a29bd8c49585963fb03ff3287788f6bd8ea30e6747a7a5

Transactions (4)

Coinbase99e11609ba141f…7a67ea618a4f72

1 in → 1 out10.5200 XPM109 B

APksWEGU…6iViiT8T

6339c954c0b8e2…907015523c0182

3 in → 1 out35.5600 XPM385 B

AeLxEQdx…Jugxqiqk

f4a35e9785bf19…c55a0a378224d9

1 in → 1 out10.4900 XPM157 B

AN7CTbAY…CXZXPsEU

d527f0259444c5…990dbda822d5e8

1 in → 2 out10.4900 XPM193 B

Aca1dndv…g4azZy2F AQ9eMWtF…mpP7gwDk

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.

1.647 × 10⁹⁸(99-digit number)

16476509692034720898…54749333876542756679

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

1.647 × 10⁹⁸(99-digit number)

16476509692034720898…54749333876542756679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.647 × 10⁹⁸(99-digit number)

16476509692034720898…54749333876542756681

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

3.295 × 10⁹⁸(99-digit number)

32953019384069441797…09498667753085513359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.295 × 10⁹⁸(99-digit number)

32953019384069441797…09498667753085513361

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

6.590 × 10⁹⁸(99-digit number)

65906038768138883595…18997335506171026719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.590 × 10⁹⁸(99-digit number)

65906038768138883595…18997335506171026721

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

1.318 × 10⁹⁹(100-digit number)

13181207753627776719…37994671012342053439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.318 × 10⁹⁹(100-digit number)

13181207753627776719…37994671012342053441

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

2.636 × 10⁹⁹(100-digit number)

26362415507255553438…75989342024684106879

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 #121,944

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