Block #1,250,854

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/24/2015, 6:32:38 AM · Difficulty 10.7753 · 5,540,668 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a496b1be47fe449ef4ce3359c704918a827f6f92fd85ab8ab58feaa37557dbb0

View on Chainz ↗

Height

#1,250,854

Difficulty

10.775343

Transactions

Size

208 B

Version

Bits

0ac67ce4

Nonce

111,757,499

Timestamp

9/24/2015, 6:32:38 AM

Confirmations

5,540,668

Merkle Root

a5ba7ba51a6485da83f28d4cc1baaa93abca0be4c2be251ff4ce530c50948859

Transactions (1)

Coinbasea5ba7ba51a6485…ce530c50948859

1 in → 1 out8.6000 XPM116 B

AJCEY9yy…tg97E6zm

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.

1.747 × 10⁹⁹(100-digit number)

17470932371024080501…00161007985077288959

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

1.747 × 10⁹⁹(100-digit number)

17470932371024080501…00161007985077288959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.747 × 10⁹⁹(100-digit number)

17470932371024080501…00161007985077288961

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

3.494 × 10⁹⁹(100-digit number)

34941864742048161002…00322015970154577919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.494 × 10⁹⁹(100-digit number)

34941864742048161002…00322015970154577921

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

6.988 × 10⁹⁹(100-digit number)

69883729484096322004…00644031940309155839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.988 × 10⁹⁹(100-digit number)

69883729484096322004…00644031940309155841

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

1.397 × 10¹⁰⁰(101-digit number)

13976745896819264400…01288063880618311679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.397 × 10¹⁰⁰(101-digit number)

13976745896819264400…01288063880618311681

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

2.795 × 10¹⁰⁰(101-digit number)

27953491793638528801…02576127761236623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.795 × 10¹⁰⁰(101-digit number)

27953491793638528801…02576127761236623361

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