Block #479,510

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 5:37:46 PM · Difficulty 10.5085 · 6,312,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac5ed7d5c4d86e8c25c15e3457a182f0747089a35b16b87a92b443b83f8f5f74

View on Chainz ↗

Height

#479,510

Difficulty

10.508461

Transactions

Size

976 B

Version

Bits

0a822a7b

Nonce

264,187

Timestamp

4/7/2014, 5:37:46 PM

Confirmations

6,312,707

Merkle Root

bd38f00f5e16bbcb977d81a8b7fccf06e06ef74dd294c01b1ed753fcf4aab50a

Transactions (2)

Coinbasece00f535ec4801…eed2eb8d274774

1 in → 1 out9.0500 XPM110 B

AeKNrjNj…1NEq95Ta

5103bcb31f561a…89864e79289484

4 in → 7 out18.4918 XPM773 B

AJJqf2Po…tRLxW6P2 AeotpmGC…wXWBzvh3 AZH3aBJB…T7FVgZ83 AVsjqzCG…L9hN77hn AeKNrjNj…1NEq95Ta

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.

7.417 × 10¹⁰¹(102-digit number)

74177558701030264371…27750106513995889919

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

7.417 × 10¹⁰¹(102-digit number)

74177558701030264371…27750106513995889919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.417 × 10¹⁰¹(102-digit number)

74177558701030264371…27750106513995889921

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

1.483 × 10¹⁰²(103-digit number)

14835511740206052874…55500213027991779839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.483 × 10¹⁰²(103-digit number)

14835511740206052874…55500213027991779841

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

2.967 × 10¹⁰²(103-digit number)

29671023480412105748…11000426055983559679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.967 × 10¹⁰²(103-digit number)

29671023480412105748…11000426055983559681

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

5.934 × 10¹⁰²(103-digit number)

59342046960824211497…22000852111967119359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.934 × 10¹⁰²(103-digit number)

59342046960824211497…22000852111967119361

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

1.186 × 10¹⁰³(104-digit number)

11868409392164842299…44001704223934238719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.186 × 10¹⁰³(104-digit number)

11868409392164842299…44001704223934238721

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