Block #1,473,310

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/27/2016, 12:20:36 AM · Difficulty 10.6917 · 5,369,559 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d24f17d641ea85cffd8b1908853c4a14f0b0d329347a941f44138badaa52feb

View on Chainz ↗

Height

#1,473,310

Difficulty

10.691739

Transactions

Size

244 B

Version

Bits

0ab115cb

Nonce

88,738,696

Timestamp

2/27/2016, 12:20:36 AM

Confirmations

5,369,559

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

8cc0e17bb6f81efe7c1091e4e0e313419ba2acd90ebabb71b9bd87b9d5792760

Transactions (1)

Coinbase8cc0e17bb6f81e…bd87b9d5792760

1 in → 2 out8.7300 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.

6.012 × 10⁹⁹(100-digit number)

60122520484110764444…02853636084522352639

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

6.012 × 10⁹⁹(100-digit number)

60122520484110764444…02853636084522352639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.012 × 10⁹⁹(100-digit number)

60122520484110764444…02853636084522352641

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

1.202 × 10¹⁰⁰(101-digit number)

12024504096822152888…05707272169044705279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.202 × 10¹⁰⁰(101-digit number)

12024504096822152888…05707272169044705281

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

2.404 × 10¹⁰⁰(101-digit number)

24049008193644305777…11414544338089410559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.404 × 10¹⁰⁰(101-digit number)

24049008193644305777…11414544338089410561

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

4.809 × 10¹⁰⁰(101-digit number)

48098016387288611555…22829088676178821119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.809 × 10¹⁰⁰(101-digit number)

48098016387288611555…22829088676178821121

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

9.619 × 10¹⁰⁰(101-digit number)

96196032774577223110…45658177352357642239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.619 × 10¹⁰⁰(101-digit number)

96196032774577223110…45658177352357642241

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 #1,473,310

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