Block #1,072,439

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2015, 4:56:25 PM · Difficulty 10.7401 · 5,734,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94f0dd318841ec9fd378b4e867e0f3954addd5bbb1d85ec660ce32b6b976a719

View on Chainz ↗

Height

#1,072,439

Difficulty

10.740105

Transactions

Size

1.01 KB

Version

Bits

0abd7783

Nonce

2,264,851,293

Timestamp

5/23/2015, 4:56:25 PM

Confirmations

5,734,143

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

736085ea59f48a3b612372c8994cc885fcf13a26b17f40daf059a312fa4866e3

Transactions (4)

Coinbase1cb798837be0c1…0a44f4e34baf66

1 in → 1 out8.6900 XPM116 B

ANSXnLY2…Sd25TjkD

a7af14e16efc48…b684b2e8fd803c

2 in → 2 out15.2523 XPM373 B

Ae9drWdk…FnLTm9Pn AS3fFHjR…1GT1Htqc

1926fb2fcc16e2…be9c6ac7a46c2c

1 in → 2 out8.6400 XPM226 B

AXrTw46X…e1dGvSFf Ac1hHJky…ut1rqMb5

73a4ce779c1111…7d44094936bfc9

1 in → 2 out6.6181 XPM225 B

Ae7YXEyn…hnSYZsCr AbTZbU6w…cbBxwB8T

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.

4.717 × 10⁹⁵(96-digit number)

47177637813399061732…09794724140481662279

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

4.717 × 10⁹⁵(96-digit number)

47177637813399061732…09794724140481662279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.717 × 10⁹⁵(96-digit number)

47177637813399061732…09794724140481662281

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

9.435 × 10⁹⁵(96-digit number)

94355275626798123464…19589448280963324559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.435 × 10⁹⁵(96-digit number)

94355275626798123464…19589448280963324561

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

1.887 × 10⁹⁶(97-digit number)

18871055125359624692…39178896561926649119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.887 × 10⁹⁶(97-digit number)

18871055125359624692…39178896561926649121

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

3.774 × 10⁹⁶(97-digit number)

37742110250719249385…78357793123853298239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.774 × 10⁹⁶(97-digit number)

37742110250719249385…78357793123853298241

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

7.548 × 10⁹⁶(97-digit number)

75484220501438498771…56715586247706596479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.548 × 10⁹⁶(97-digit number)

75484220501438498771…56715586247706596481

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 #1,072,439

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