Block #1,570,497

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2016, 8:11:49 PM · Difficulty 10.7480 · 5,263,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0e758ed706be96519e10fdc08d4bab2dc6d160322dbc91f8881825ecec821186

View on Chainz ↗

Height

#1,570,497

Difficulty

10.748042

Transactions

Size

871 B

Version

Bits

0abf7fae

Nonce

209,103,334

Timestamp

5/3/2016, 8:11:49 PM

Confirmations

5,263,244

Mined by

⛏️ P2SHAMeNJrG4TrhghcBtGp6LnooGbGcwukoRYH

Merkle Root

804b99d392bcb90f886c0765d531d7a993fe283008871edb88a21f3d192892e8

Transactions (2)

Coinbase6b0c62c6029082…6f9142e3eb17f9

1 in → 1 out8.6500 XPM110 B

AMeNJrG4…cwukoRYH

f7300ae890fa06…53ca2bc1677291

4 in → 2 out0.7954 XPM671 B

AKEcSLWL…pgLbUcoM ALGhUmkv…BXUe6EjM

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.

2.577 × 10⁹⁵(96-digit number)

25771196292700176120…51839192589684669439

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

2.577 × 10⁹⁵(96-digit number)

25771196292700176120…51839192589684669439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.577 × 10⁹⁵(96-digit number)

25771196292700176120…51839192589684669441

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

5.154 × 10⁹⁵(96-digit number)

51542392585400352241…03678385179369338879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.154 × 10⁹⁵(96-digit number)

51542392585400352241…03678385179369338881

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

1.030 × 10⁹⁶(97-digit number)

10308478517080070448…07356770358738677759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.030 × 10⁹⁶(97-digit number)

10308478517080070448…07356770358738677761

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

2.061 × 10⁹⁶(97-digit number)

20616957034160140896…14713540717477355519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.061 × 10⁹⁶(97-digit number)

20616957034160140896…14713540717477355521

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

4.123 × 10⁹⁶(97-digit number)

41233914068320281793…29427081434954711039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.123 × 10⁹⁶(97-digit number)

41233914068320281793…29427081434954711041

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 #1,570,497

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