Block #70,536

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 2:06:33 PM · Difficulty 8.9923 · 6,725,437 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e618ab58e56fa4c026fc3714f6c21627cf53dc250d2081085a348362d06aeb49

View on Chainz ↗

Height

#70,536

Difficulty

8.992259

Transactions

Size

838 B

Version

Bits

08fe04ac

Nonce

Timestamp

7/20/2013, 2:06:33 PM

Confirmations

6,725,437

Mined by

⛏️ P2SHAapoTsdy3gAuw6PyiSxU6FRAg4JDZNnMx1

Merkle Root

0053ca5674585bf8bb4429583a2b5a00140a1fe505c51cb14fe9ffe5b9b8e829

Transactions (2)

Coinbaseddf0893bbe957e…26067e61609fd8

1 in → 1 out12.3600 XPM110 B

AapoTsdy…JDZNnMx1

79c999a31a7c9a…b19d1879752585

4 in → 1 out3300.0000 XPM637 B

APLFNzuP…SNqTbuEY

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.

1.471 × 10⁹⁶(97-digit number)

14718066348145365489…54596460487074999439

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

1.471 × 10⁹⁶(97-digit number)

14718066348145365489…54596460487074999439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.471 × 10⁹⁶(97-digit number)

14718066348145365489…54596460487074999441

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

2.943 × 10⁹⁶(97-digit number)

29436132696290730979…09192920974149998879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.943 × 10⁹⁶(97-digit number)

29436132696290730979…09192920974149998881

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

5.887 × 10⁹⁶(97-digit number)

58872265392581461958…18385841948299997759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.887 × 10⁹⁶(97-digit number)

58872265392581461958…18385841948299997761

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

1.177 × 10⁹⁷(98-digit number)

11774453078516292391…36771683896599995519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.177 × 10⁹⁷(98-digit number)

11774453078516292391…36771683896599995521

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

2.354 × 10⁹⁷(98-digit number)

23548906157032584783…73543367793199991039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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