Block #477,624

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 1:48:09 PM · Difficulty 10.4860 · 6,320,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

895fe133909d1d6422132199f508777dbe6b8964fa2b78e1a141ae3d5d8352ea

View on Chainz ↗

Height

#477,624

Difficulty

10.486038

Transactions

Size

1.67 KB

Version

Bits

0a7c6cf6

Nonce

32,199

Timestamp

4/6/2014, 1:48:09 PM

Confirmations

6,320,758

Mined by

⛏️ IAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

a6b0d166c5296c624c949632d3dce4ffd4138c80d4d0d0a9ec2f5739899d588d

Transactions (2)

Coinbase9cec0cd0dc852d…957b2d3ec9e8b7

1 in → 20 out9.0900 XPM743 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AbHY4iza…Yckt2J5W ATp4jJhs…TbSgR8Qb

19c39e2e1716ec…516495727230da

4 in → 12 out36.5900 XPM875 B

ANcmVbm3…w2hY6zXn AGEE6Zjb…JEXkMfEx ALC1VQzr…2tnpfMyB AS791b91…2oFChkDv AJTZmWMz…K4xGSLcs

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.

2.708 × 10⁹⁶(97-digit number)

27084751001617783192…72123665945845328239

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

2.708 × 10⁹⁶(97-digit number)

27084751001617783192…72123665945845328239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.708 × 10⁹⁶(97-digit number)

27084751001617783192…72123665945845328241

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

5.416 × 10⁹⁶(97-digit number)

54169502003235566384…44247331891690656479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.416 × 10⁹⁶(97-digit number)

54169502003235566384…44247331891690656481

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

1.083 × 10⁹⁷(98-digit number)

10833900400647113276…88494663783381312959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.083 × 10⁹⁷(98-digit number)

10833900400647113276…88494663783381312961

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

2.166 × 10⁹⁷(98-digit number)

21667800801294226553…76989327566762625919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.166 × 10⁹⁷(98-digit number)

21667800801294226553…76989327566762625921

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

4.333 × 10⁹⁷(98-digit number)

43335601602588453107…53978655133525251839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.333 × 10⁹⁷(98-digit number)

43335601602588453107…53978655133525251841

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