Block #76,140

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 9:55:25 PM · Difficulty 9.0738 · 6,713,619 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b388e807f034174876598489e6b16051b9c86a6efe7103b2af3e9500619806c

View on Chainz ↗

Height

#76,140

Difficulty

9.073769

Transactions

Size

428 B

Version

Bits

0912e289

Nonce

Timestamp

7/21/2013, 9:55:25 PM

Confirmations

6,713,619

Merkle Root

3bfce03f8d21c84ffa5af1fa899e2743fc01d9af6e13e2fed74b95bb68a87a78

Transactions (2)

Coinbasebde0a02c5d4ed0…f143b18c98b524

1 in → 1 out12.1400 XPM110 B

AcVEwGKo…e1BBkAMj

f96a37ce2cd18e…f5da62f6506b9d

1 in → 2 out110.0689 XPM226 B

AVEKu4Ai…xucwuXDZ AL5iHwkH…YGkGxDZC

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.

5.705 × 10⁹⁹(100-digit number)

57058267683279424666…04197530287301706939

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

5.705 × 10⁹⁹(100-digit number)

57058267683279424666…04197530287301706939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.705 × 10⁹⁹(100-digit number)

57058267683279424666…04197530287301706941

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

1.141 × 10¹⁰⁰(101-digit number)

11411653536655884933…08395060574603413879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.141 × 10¹⁰⁰(101-digit number)

11411653536655884933…08395060574603413881

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

2.282 × 10¹⁰⁰(101-digit number)

22823307073311769866…16790121149206827759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.282 × 10¹⁰⁰(101-digit number)

22823307073311769866…16790121149206827761

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

4.564 × 10¹⁰⁰(101-digit number)

45646614146623539733…33580242298413655519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.564 × 10¹⁰⁰(101-digit number)

45646614146623539733…33580242298413655521

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

9.129 × 10¹⁰⁰(101-digit number)

91293228293247079466…67160484596827311039

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