Block #1,471,478

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2016, 12:50:34 PM · Difficulty 10.7093 · 5,371,418 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3924d1d93a2f0215ea53daa18343df694200c939d9e98db472db527be8ef9f7c

View on Chainz ↗

Height

#1,471,478

Difficulty

10.709287

Transactions

Size

244 B

Version

Bits

0ab593d2

Nonce

547,889,476

Timestamp

2/25/2016, 12:50:34 PM

Confirmations

5,371,418

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

5e25e143e3418c3e559b974ee398b46db0670db6bdb74988add212cd2ce59aa1

Transactions (1)

Coinbase5e25e143e3418c…d212cd2ce59aa1

1 in → 2 out8.7100 XPM152 B

AdwKJkgS…L2zsc2ej ALPu3s2c…EJXLjVFh

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.

5.968 × 10⁹⁹(100-digit number)

59680887152059527619…88649883688423096319

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

5.968 × 10⁹⁹(100-digit number)

59680887152059527619…88649883688423096319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.968 × 10⁹⁹(100-digit number)

59680887152059527619…88649883688423096321

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

1.193 × 10¹⁰⁰(101-digit number)

11936177430411905523…77299767376846192639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.193 × 10¹⁰⁰(101-digit number)

11936177430411905523…77299767376846192641

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

2.387 × 10¹⁰⁰(101-digit number)

23872354860823811047…54599534753692385279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.387 × 10¹⁰⁰(101-digit number)

23872354860823811047…54599534753692385281

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

4.774 × 10¹⁰⁰(101-digit number)

47744709721647622095…09199069507384770559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.774 × 10¹⁰⁰(101-digit number)

47744709721647622095…09199069507384770561

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

9.548 × 10¹⁰⁰(101-digit number)

95489419443295244190…18398139014769541119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.548 × 10¹⁰⁰(101-digit number)

95489419443295244190…18398139014769541121

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 #1,471,478

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