Block #37,612

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 10:53:21 AM · Difficulty 8.0514 · 6,752,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d4fedae3757910f31ab57dcca0626b22d6fe62ff09ac10f7d596754c135a583

View on Chainz ↗

Height

#37,612

Difficulty

8.051439

Transactions

Size

572 B

Version

Bits

080d2b1d

Nonce

744

Timestamp

7/14/2013, 10:53:21 AM

Confirmations

6,752,137

Merkle Root

ee3f45ecb294cd4516b3732c8d06ed184590ac6ec425bf6db7e694cdb1b5665e

Transactions (2)

Coinbase68e27f7376801b…385dab1ee236e4

1 in → 1 out15.4200 XPM109 B

AM9hFbZp…p3u823iM

50a7cb2aa613b3…f855e77c89bf2c

2 in → 2 out26.6500 XPM374 B

Abjz3Cii…jjHshsh8 AHUbt4Ww…hcxVK8Cp

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.

8.342 × 10⁹¹(92-digit number)

83420126923893173665…97680619853338482919

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

8.342 × 10⁹¹(92-digit number)

83420126923893173665…97680619853338482919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.342 × 10⁹¹(92-digit number)

83420126923893173665…97680619853338482921

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

1.668 × 10⁹²(93-digit number)

16684025384778634733…95361239706676965839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.668 × 10⁹²(93-digit number)

16684025384778634733…95361239706676965841

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

3.336 × 10⁹²(93-digit number)

33368050769557269466…90722479413353931679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.336 × 10⁹²(93-digit number)

33368050769557269466…90722479413353931681

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

6.673 × 10⁹²(93-digit number)

66736101539114538932…81444958826707863359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.673 × 10⁹²(93-digit number)

66736101539114538932…81444958826707863361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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