Block #195,783

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/6/2013, 1:12:34 AM · Difficulty 9.8806 · 6,614,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b07192e4350ef7c96037e87f5e8143d5014131d16ed5e0df3da650126ccef41

View on Chainz ↗

Height

#195,783

Difficulty

9.880553

Transactions

Size

2.47 KB

Version

Bits

09e16bed

Nonce

1,165,451,153

Timestamp

10/6/2013, 1:12:34 AM

Confirmations

6,614,667

Mined by

⛏️ RPvAZ1SeNMMM8zFm1R3hsXNth1bmJ6tkj61SE

Merkle Root

279c734dba65c67e80738358774a1c27d573d5458a4806b6ba4558e64578a0c8

Transactions (1)

Coinbase279c734dba65c6…4558e64578a0c8

1 in → 70 out10.2000 XPM2.38 KB

AZ1SeNMM…6tkj61SE ANBtDhv7…saWQoBRP AQjqwnU7…GwpNSJWX AewGmqcv…8ZoEhTt9 ANxERLYc…v7fC1vqc

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.

7.278 × 10⁹²(93-digit number)

72783047912898083203…45538764964876563199

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

7.278 × 10⁹²(93-digit number)

72783047912898083203…45538764964876563199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.278 × 10⁹²(93-digit number)

72783047912898083203…45538764964876563201

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

1.455 × 10⁹³(94-digit number)

14556609582579616640…91077529929753126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.455 × 10⁹³(94-digit number)

14556609582579616640…91077529929753126401

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

2.911 × 10⁹³(94-digit number)

29113219165159233281…82155059859506252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.911 × 10⁹³(94-digit number)

29113219165159233281…82155059859506252801

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

5.822 × 10⁹³(94-digit number)

58226438330318466562…64310119719012505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.822 × 10⁹³(94-digit number)

58226438330318466562…64310119719012505601

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

1.164 × 10⁹⁴(95-digit number)

11645287666063693312…28620239438025011199

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

Block #195,783

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