Block #1,409,734

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2016, 5:11:06 AM · Difficulty 10.8056 · 5,417,402 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

024c0f786e63489684f438255daaea3f7e484be3f68367b16e07be7277b46d98

View on Chainz ↗

Height

#1,409,734

Difficulty

10.805609

Transactions

Size

1.01 KB

Version

Bits

0ace3c62

Nonce

310,780,423

Timestamp

1/12/2016, 5:11:06 AM

Confirmations

5,417,402

Mined by

⛏️ P2SHAXzAtjZoVQLNzdcvTZaUwZqX72qj5iNrTk

Merkle Root

024e0a9b2e4ec2b7648acc8dc66a653294717ab8e48c236380de4aa8a3f683a3

Transactions (2)

Coinbaseb157d70fd518e0…1c1ccc884f473a

1 in → 1 out8.5600 XPM110 B

AXzAtjZo…qj5iNrTk

0523de3f8c9e21…157c2711c9405b

1 in → 20 out61.1612 XPM838 B

AT9ngrHa…L1nnNKSX AQ2Run6n…XwPQARbJ AT3ih8hC…3BVRX71B AZiFi5Xe…2mZ2aske AUv7W8VK…gCBRLqz3

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.

4.571 × 10⁹⁵(96-digit number)

45715021689178012370…20449206019445227519

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

4.571 × 10⁹⁵(96-digit number)

45715021689178012370…20449206019445227519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.571 × 10⁹⁵(96-digit number)

45715021689178012370…20449206019445227521

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

9.143 × 10⁹⁵(96-digit number)

91430043378356024740…40898412038890455039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.143 × 10⁹⁵(96-digit number)

91430043378356024740…40898412038890455041

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

1.828 × 10⁹⁶(97-digit number)

18286008675671204948…81796824077780910079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.828 × 10⁹⁶(97-digit number)

18286008675671204948…81796824077780910081

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

3.657 × 10⁹⁶(97-digit number)

36572017351342409896…63593648155561820159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.657 × 10⁹⁶(97-digit number)

36572017351342409896…63593648155561820161

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

7.314 × 10⁹⁶(97-digit number)

73144034702684819792…27187296311123640319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.314 × 10⁹⁶(97-digit number)

73144034702684819792…27187296311123640321

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 #1,409,734

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