Block #648,515

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/26/2014, 8:53:43 AM · Difficulty 10.9515 · 6,164,438 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

71e6295587014e11dec6fd3063d6150a4d90ab314159e328148b44d00ed94535

View on Chainz ↗

Height

#648,515

Difficulty

10.951536

Transactions

Size

3.87 KB

Version

Bits

0af397e3

Nonce

351,469,699

Timestamp

7/26/2014, 8:53:43 AM

Confirmations

6,164,438

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f31dd444f89e3acbd1fa50e83a66a372c2fcac362db5d18361ed7f15c51afe5e

Transactions (4)

Coinbase395d382269044f…d616ce6d09e73c

1 in → 1 out8.4000 XPM116 B

ANSXnLY2…Sd25TjkD

21c7b9ff5be169…61527c9b16941d

18 in → 1 out499.9900 XPM2.65 KB

AY6zxofy…SaX3wdQn

3909a1b610a31f…f80f2a32ef9bbe

5 in → 2 out10.0528 XPM820 B

Adsdktbi…qQMZ5eiC AY5Fezp3…pXXwWzip

feca1b2bec9e6b…6b0e4c5a98ed20

1 in → 2 out4.4097 XPM226 B

ANjspYdJ…SHV1niHp Ae7YXEyn…hnSYZsCr

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.

8.734 × 10⁹⁴(95-digit number)

87346260682951013511…46047531524209509039

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

8.734 × 10⁹⁴(95-digit number)

87346260682951013511…46047531524209509039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.734 × 10⁹⁴(95-digit number)

87346260682951013511…46047531524209509041

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

1.746 × 10⁹⁵(96-digit number)

17469252136590202702…92095063048419018079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.746 × 10⁹⁵(96-digit number)

17469252136590202702…92095063048419018081

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

3.493 × 10⁹⁵(96-digit number)

34938504273180405404…84190126096838036159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.493 × 10⁹⁵(96-digit number)

34938504273180405404…84190126096838036161

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

6.987 × 10⁹⁵(96-digit number)

69877008546360810809…68380252193676072319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.987 × 10⁹⁵(96-digit number)

69877008546360810809…68380252193676072321

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

1.397 × 10⁹⁶(97-digit number)

13975401709272162161…36760504387352144639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.397 × 10⁹⁶(97-digit number)

13975401709272162161…36760504387352144641

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #648,515

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