Block #103,185

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/7/2013, 11:37:55 AM · Difficulty 9.5179 · 6,701,743 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3571d1066724122e235cd7d1155d1229aa12cf4dc0dca361cdf067e77faaa0e8

View on Chainz ↗

Height

#103,185

Difficulty

9.517911

Transactions

Size

546 B

Version

Bits

098495cd

Nonce

128,164

Timestamp

8/7/2013, 11:37:55 AM

Confirmations

6,701,743

Mined by

⛏️ P2SHAR9jijg8jaCFCUWK7HPiXHXgswE51RaC7H

Merkle Root

8b1e7ed297f98220fd82dc6641002c0d0a75e3e718dcd9299365e7fb37a6a020

Transactions (2)

Coinbase50117962465469…397cf86693a6b6

1 in → 1 out11.0300 XPM109 B

AR9jijg8…E51RaC7H

fc7e38b4ff7574…9c4129a935feed

2 in → 2 out11.4600 XPM340 B

AVHerDaj…BgiLTrnC AKt1xoQp…cNapFdsX

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.

3.119 × 10¹¹¹(112-digit number)

31194209833295892100…64245718268164307579

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

3.119 × 10¹¹¹(112-digit number)

31194209833295892100…64245718268164307579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.119 × 10¹¹¹(112-digit number)

31194209833295892100…64245718268164307581

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

6.238 × 10¹¹¹(112-digit number)

62388419666591784200…28491436536328615159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.238 × 10¹¹¹(112-digit number)

62388419666591784200…28491436536328615161

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

1.247 × 10¹¹²(113-digit number)

12477683933318356840…56982873072657230319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.247 × 10¹¹²(113-digit number)

12477683933318356840…56982873072657230321

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

2.495 × 10¹¹²(113-digit number)

24955367866636713680…13965746145314460639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.495 × 10¹¹²(113-digit number)

24955367866636713680…13965746145314460641

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

4.991 × 10¹¹²(113-digit number)

49910735733273427360…27931492290628921279

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