Block #170,983

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/19/2013, 4:16:20 AM · Difficulty 9.8647 · 6,621,794 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62411fa10bd29aad6faab9565737d0d98f2bc492d4bfe95cf7412b38d5a099bc

View on Chainz ↗

Height

#170,983

Difficulty

9.864709

Transactions

Size

571 B

Version

Bits

09dd5d8b

Nonce

16,581

Timestamp

9/19/2013, 4:16:20 AM

Confirmations

6,621,794

Merkle Root

0a52dccec9edde12772c4f41ce80e93d56a9d724d4048e0807e5de2dfec6dcfd

Transactions (2)

Coinbaseb6da7482abdd78…954d966681189c

1 in → 1 out10.2700 XPM109 B

AP91QEDQ…W6JZAB9n

f95f4e7b9313b2…c2cf6c8244f81f

2 in → 2 out10.3769 XPM372 B

ALpthvGg…D1g5z4CT Ab7xnpLH…HV8Ag5j2

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.

3.058 × 10⁹⁴(95-digit number)

30586388956206370799…41613093630086098879

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

3.058 × 10⁹⁴(95-digit number)

30586388956206370799…41613093630086098879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.058 × 10⁹⁴(95-digit number)

30586388956206370799…41613093630086098881

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

6.117 × 10⁹⁴(95-digit number)

61172777912412741598…83226187260172197759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.117 × 10⁹⁴(95-digit number)

61172777912412741598…83226187260172197761

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

1.223 × 10⁹⁵(96-digit number)

12234555582482548319…66452374520344395519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.223 × 10⁹⁵(96-digit number)

12234555582482548319…66452374520344395521

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

2.446 × 10⁹⁵(96-digit number)

24469111164965096639…32904749040688791039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.446 × 10⁹⁵(96-digit number)

24469111164965096639…32904749040688791041

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

4.893 × 10⁹⁵(96-digit number)

48938222329930193278…65809498081377582079

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