Block #69,188

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 7:34:24 AM · Difficulty 8.9906 · 6,721,800 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

597bd044b5b6275ccd731a76442bb2d589cd9f2405d3977ed64c130a65dfc6f7

View on Chainz ↗

Height

#69,188

Difficulty

8.990597

Transactions

Size

199 B

Version

Bits

08fd97c6

Nonce

640

Timestamp

7/20/2013, 7:34:24 AM

Confirmations

6,721,800

Merkle Root

0980a7f7929c35f917ea173d138d7af3a6541ef7cff6a342bfdde9da070594db

Transactions (1)

Coinbase0980a7f7929c35…dde9da070594db

1 in → 1 out12.3500 XPM110 B

AXSFye4r…ADf1YWCU

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.

1.693 × 10⁹³(94-digit number)

16939434147890382812…25085457478695109899

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

1.693 × 10⁹³(94-digit number)

16939434147890382812…25085457478695109899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.693 × 10⁹³(94-digit number)

16939434147890382812…25085457478695109901

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

3.387 × 10⁹³(94-digit number)

33878868295780765625…50170914957390219799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.387 × 10⁹³(94-digit number)

33878868295780765625…50170914957390219801

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

6.775 × 10⁹³(94-digit number)

67757736591561531250…00341829914780439599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.775 × 10⁹³(94-digit number)

67757736591561531250…00341829914780439601

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

1.355 × 10⁹⁴(95-digit number)

13551547318312306250…00683659829560879199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.355 × 10⁹⁴(95-digit number)

13551547318312306250…00683659829560879201

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

2.710 × 10⁹⁴(95-digit number)

27103094636624612500…01367319659121758399

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