Block #625,004

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/9/2014, 9:49:19 AM · Difficulty 10.9588 · 6,199,883 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

579da192a9923d5d382d699f96088da960c469f3459e8616c1f1e470b74b80ab

View on Chainz ↗

Height

#625,004

Difficulty

10.958805

Transactions

Size

1.44 KB

Version

Bits

0af57443

Nonce

276,032,299

Timestamp

7/9/2014, 9:49:19 AM

Confirmations

6,199,883

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

dee26b25c5950e55b5dd97f3016a783a766a58e9d4d69c23beb46cc79e5d1275

Transactions (4)

Coinbase0a58134e3a9a16…57b8db35f8b826

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

0390a1cbfce384…dc70283bef4ca9

2 in → 2 out15.6295 XPM375 B

AKdVnGNx…Qrwef9uk AHKyhKvK…Z2hFkpuR

f2ff085d27cc0b…a23996ca3fc613

4 in → 2 out20.0136 XPM670 B

AKQb78kd…kP7kYNJq AerHzLX5…UVJ4PHfY

7a02e065584867…30c94cf9de070f

1 in → 2 out5.5205 XPM226 B

AXbhTQbx…4k632dyJ AXme6eTz…PLdysKBL

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.

1.293 × 10⁹⁸(99-digit number)

12939997370278657432…40010227617351639039

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

1.293 × 10⁹⁸(99-digit number)

12939997370278657432…40010227617351639039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.293 × 10⁹⁸(99-digit number)

12939997370278657432…40010227617351639041

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

2.587 × 10⁹⁸(99-digit number)

25879994740557314865…80020455234703278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.587 × 10⁹⁸(99-digit number)

25879994740557314865…80020455234703278081

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

5.175 × 10⁹⁸(99-digit number)

51759989481114629730…60040910469406556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.175 × 10⁹⁸(99-digit number)

51759989481114629730…60040910469406556161

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

1.035 × 10⁹⁹(100-digit number)

10351997896222925946…20081820938813112319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.035 × 10⁹⁹(100-digit number)

10351997896222925946…20081820938813112321

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

2.070 × 10⁹⁹(100-digit number)

20703995792445851892…40163641877626224639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.070 × 10⁹⁹(100-digit number)

20703995792445851892…40163641877626224641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.140 × 10⁹⁹(100-digit number)

41407991584891703784…80327283755252449279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #625,004

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