Block #1,503,540

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2016, 11:04:53 AM · Difficulty 10.6502 · 5,314,036 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4312ee4b6126040ca1c9bb6f466fc873b9b1a5a5207410ba42e468af892e979

View on Chainz ↗

Height

#1,503,540

Difficulty

10.650239

Transactions

Size

1.11 KB

Version

Bits

0aa67610

Nonce

406,003,156

Timestamp

3/19/2016, 11:04:53 AM

Confirmations

5,314,036

Mined by

⛏️ P2SHAcT76gNek8pge7rd487H2reREFpnLaQ7m9

Merkle Root

1d7cda300de570ca876a3ae063ddca264d76105de9c0165f90626076e56659a9

Transactions (2)

Coinbased117a93ecaf2d3…56ffdbe8696cb0

1 in → 1 out8.8100 XPM109 B

AcT76gNe…pnLaQ7m9

dbb4387fc3b1ac…7c93bd80875800

1 in → 23 out13.4199 XPM940 B

AaGVrsTD…en81cV6L AZKDFbue…W3u6CJGH AYXTz78e…RfsWmrAH AYqPum2Q…NmRxpZGi AddUSmgB…nsNX1H2E

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.

3.267 × 10⁹⁶(97-digit number)

32678834024045596626…81335334920194378239

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

3.267 × 10⁹⁶(97-digit number)

32678834024045596626…81335334920194378239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.267 × 10⁹⁶(97-digit number)

32678834024045596626…81335334920194378241

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

6.535 × 10⁹⁶(97-digit number)

65357668048091193252…62670669840388756479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.535 × 10⁹⁶(97-digit number)

65357668048091193252…62670669840388756481

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

1.307 × 10⁹⁷(98-digit number)

13071533609618238650…25341339680777512959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.307 × 10⁹⁷(98-digit number)

13071533609618238650…25341339680777512961

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

2.614 × 10⁹⁷(98-digit number)

26143067219236477300…50682679361555025919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.614 × 10⁹⁷(98-digit number)

26143067219236477300…50682679361555025921

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

5.228 × 10⁹⁷(98-digit number)

52286134438472954601…01365358723110051839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.228 × 10⁹⁷(98-digit number)

52286134438472954601…01365358723110051841

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 #1,503,540

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