Block #73,800

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 7:53:09 AM · Difficulty 8.9951 · 6,724,772 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5fc634377a58ef25b3e8c056a01d0517ee1c8ec4cac08e7c7d8519279d8e2efe

View on Chainz ↗

Height

#73,800

Difficulty

8.995074

Transactions

Size

868 B

Version

Bits

08febd2c

Nonce

587

Timestamp

7/21/2013, 7:53:09 AM

Confirmations

6,724,772

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

3505a598d4667fb92b59e931b2e3cc87c36ea9f9f4f46fd7b7dfbb17a3d1e2d6

Transactions (2)

Coinbaseceee50d7f51573…e8a16dbc90d7aa

1 in → 1 out12.3500 XPM110 B

ANey87HK…MGUx5bYr

cbbeb8d415f843…de770e6c035813

4 in → 2 out94.7494 XPM669 B

AJ6X8FCs…nqeLo6HM ALUVg4QQ…r3SnUqFN

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.

4.945 × 10⁹¹(92-digit number)

49459784730142540327…14844391464687006509

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

4.945 × 10⁹¹(92-digit number)

49459784730142540327…14844391464687006509

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.945 × 10⁹¹(92-digit number)

49459784730142540327…14844391464687006511

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

9.891 × 10⁹¹(92-digit number)

98919569460285080654…29688782929374013019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.891 × 10⁹¹(92-digit number)

98919569460285080654…29688782929374013021

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

1.978 × 10⁹²(93-digit number)

19783913892057016130…59377565858748026039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.978 × 10⁹²(93-digit number)

19783913892057016130…59377565858748026041

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

3.956 × 10⁹²(93-digit number)

39567827784114032261…18755131717496052079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.956 × 10⁹²(93-digit number)

39567827784114032261…18755131717496052081

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

7.913 × 10⁹²(93-digit number)

79135655568228064523…37510263434992104159

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