Block #486,990

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 9:36:52 PM · Difficulty 10.6348 · 6,316,053 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81a258c00e573608c65104f552b976ba07bbf2ccb1acd34ef021893e78447e2b

View on Chainz ↗

Height

#486,990

Difficulty

10.634829

Transactions

Size

1.54 KB

Version

Bits

0aa2842a

Nonce

24,503

Timestamp

4/11/2014, 9:36:52 PM

Confirmations

6,316,053

Mined by

⛏️ NnQAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

49c118c72c14cbb08bff97c38d2ed8a92ae2f098c5fefd021460d07f1ceef90d

Transactions (4)

Coinbase09c26523a65a9b…cc9f95c8f8e76d

1 in → 22 out8.8600 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm ATp4jJhs…TbSgR8Qb AMW1p9oT…2TzdaZxH

5412e6295bfd18…d0a118599b7c8c

1 in → 2 out7.9179 XPM225 B

AG9Gf7iz…jNpvssxS AJv8hJMD…wnan8kAg

7d768d2a426db0…543140c5d84dda

1 in → 2 out7.9110 XPM226 B

AdJ74Yje…ehZYPasg AXiN448S…vbShp5d5

9e75d0b8b69189…6b6ed1c7bad3ba

1 in → 2 out7.9115 XPM227 B

AU3Hcwi2…XBfnpRDa AQ7MjUsR…fJoaCvvR

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.

3.463 × 10⁹⁶(97-digit number)

34639900311997387361…10208118023290663679

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

3.463 × 10⁹⁶(97-digit number)

34639900311997387361…10208118023290663679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.463 × 10⁹⁶(97-digit number)

34639900311997387361…10208118023290663681

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

6.927 × 10⁹⁶(97-digit number)

69279800623994774722…20416236046581327359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.927 × 10⁹⁶(97-digit number)

69279800623994774722…20416236046581327361

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

1.385 × 10⁹⁷(98-digit number)

13855960124798954944…40832472093162654719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.385 × 10⁹⁷(98-digit number)

13855960124798954944…40832472093162654721

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

2.771 × 10⁹⁷(98-digit number)

27711920249597909889…81664944186325309439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.771 × 10⁹⁷(98-digit number)

27711920249597909889…81664944186325309441

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

5.542 × 10⁹⁷(98-digit number)

55423840499195819778…63329888372650618879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.542 × 10⁹⁷(98-digit number)

55423840499195819778…63329888372650618881

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