Block #119,772

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/16/2013, 5:07:03 PM · Difficulty 9.7504 · 6,691,375 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d66f966b7839d28c2d64a2cbc0c1d2a3a27be56f3380ae9e710ea4be5da994c7

View on Chainz ↗

Height

#119,772

Difficulty

9.750422

Transactions

Size

956 B

Version

Bits

09c01bab

Nonce

973,544

Timestamp

8/16/2013, 5:07:03 PM

Confirmations

6,691,375

Mined by

⛏️ P2SHAYyPPXgF5A3RKbdbyWYgDSxAkdb6nr5cD2

Merkle Root

7d558c5b0b3a3598e89ea3bf8bace60a56b37dd8c73f199c66981182d87b6181

Transactions (4)

Coinbase2f12214bc86016…2ec3c3ee7ec3fe

1 in → 1 out10.5300 XPM109 B

AYyPPXgF…b6nr5cD2

03c1505861fadf…593ca1d3b5e33a

2 in → 2 out199.3371 XPM372 B

AZtQHBSJ…ZB8bwi8M AQSJqCfp…3EUzHBTj

79ecfc5f9edf09…e8afde48d13d52

1 in → 1 out10.6700 XPM158 B

AY5L1chV…SqfWvt6Z

277c4a1c8a18d5…5927391351c8a3

1 in → 2 out10.5000 XPM227 B

AcuFDx2A…qXJK3kce ARu3MBmR…93UxSZM9

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.

1.189 × 10⁹⁵(96-digit number)

11891352764993927994…69668974341873118159

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

1.189 × 10⁹⁵(96-digit number)

11891352764993927994…69668974341873118159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.189 × 10⁹⁵(96-digit number)

11891352764993927994…69668974341873118161

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

2.378 × 10⁹⁵(96-digit number)

23782705529987855988…39337948683746236319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.378 × 10⁹⁵(96-digit number)

23782705529987855988…39337948683746236321

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

4.756 × 10⁹⁵(96-digit number)

47565411059975711977…78675897367492472639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.756 × 10⁹⁵(96-digit number)

47565411059975711977…78675897367492472641

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

9.513 × 10⁹⁵(96-digit number)

95130822119951423954…57351794734984945279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.513 × 10⁹⁵(96-digit number)

95130822119951423954…57351794734984945281

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

1.902 × 10⁹⁶(97-digit number)

19026164423990284790…14703589469969890559

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 #119,772

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