Block #486,877

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 8:03:56 PM · Difficulty 10.6337 · 6,316,342 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

980d61751b9fa4cfe5b6046a992610f8b68aefdeeb6f1c8e1603046c29ca4dac

View on Chainz ↗

Height

#486,877

Difficulty

10.633694

Transactions

Size

583 B

Version

Bits

0aa239cb

Nonce

116,400,282

Timestamp

4/11/2014, 8:03:56 PM

Confirmations

6,316,342

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

62e39f267c054e0c83f9368892c4def9bd7dcfe9be365381fd701a69dbb5da8b

Transactions (2)

Coinbasece7cf2924ecb9d…ae1bc2d47ff711

1 in → 1 out8.8400 XPM116 B

AbwWkWZt…kawDhufa

d9157f1a29ec29…3e8c031754113e

2 in → 2 out13.0602 XPM375 B

ASsiutoe…8AhBiX83 AHoeFhv6…b2j3yLe2

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.

2.756 × 10⁹⁸(99-digit number)

27564821643364441994…30154516070185968639

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

2.756 × 10⁹⁸(99-digit number)

27564821643364441994…30154516070185968639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.756 × 10⁹⁸(99-digit number)

27564821643364441994…30154516070185968641

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

5.512 × 10⁹⁸(99-digit number)

55129643286728883988…60309032140371937279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.512 × 10⁹⁸(99-digit number)

55129643286728883988…60309032140371937281

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

1.102 × 10⁹⁹(100-digit number)

11025928657345776797…20618064280743874559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.102 × 10⁹⁹(100-digit number)

11025928657345776797…20618064280743874561

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

2.205 × 10⁹⁹(100-digit number)

22051857314691553595…41236128561487749119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.205 × 10⁹⁹(100-digit number)

22051857314691553595…41236128561487749121

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

4.410 × 10⁹⁹(100-digit number)

44103714629383107190…82472257122975498239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.410 × 10⁹⁹(100-digit number)

44103714629383107190…82472257122975498241

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