Block #624,821

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/9/2014, 7:06:03 AM · Difficulty 10.9586 · 6,182,373 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01dbc22cea3bfdcf02070a0ed471c48cc8df7cf139506fa3e877fedc00ca5d7c

View on Chainz ↗

Height

#624,821

Difficulty

10.958644

Transactions

Size

20.93 KB

Version

Bits

0af569b0

Nonce

452,081,629

Timestamp

7/9/2014, 7:06:03 AM

Confirmations

6,182,373

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0656e8d14e928155e327fa17188c98bf8b53d33bfdadc8525efd6197e538448e

Transactions (3)

Coinbasefc07c6ce0e26ac…644642dc67df57

1 in → 1 out8.5400 XPM116 B

ANSXnLY2…Sd25TjkD

db2deb8f039120…006568c09dccf5

92 in → 308 out768.4692 XPM20.51 KB

AGmJTaBE…BAYN1c8c ARnrKgkF…2MW7rRXC AaMussGv…3zs22MvK AUP75Q1W…DfeqV2e9 ALWwCSJA…MALZUd1H

44368f61dfbf5b…9cb903f546e80c

1 in → 2 out1.1788 XPM226 B

AXme6eTz…PLdysKBL AMfUDzQV…2jsnaxky

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.

2.109 × 10⁹⁵(96-digit number)

21093754862336804418…42268030458366519659

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

2.109 × 10⁹⁵(96-digit number)

21093754862336804418…42268030458366519659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.109 × 10⁹⁵(96-digit number)

21093754862336804418…42268030458366519661

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

4.218 × 10⁹⁵(96-digit number)

42187509724673608836…84536060916733039319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.218 × 10⁹⁵(96-digit number)

42187509724673608836…84536060916733039321

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

8.437 × 10⁹⁵(96-digit number)

84375019449347217673…69072121833466078639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.437 × 10⁹⁵(96-digit number)

84375019449347217673…69072121833466078641

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

1.687 × 10⁹⁶(97-digit number)

16875003889869443534…38144243666932157279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.687 × 10⁹⁶(97-digit number)

16875003889869443534…38144243666932157281

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

3.375 × 10⁹⁶(97-digit number)

33750007779738887069…76288487333864314559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.375 × 10⁹⁶(97-digit number)

33750007779738887069…76288487333864314561

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 #624,821

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