Block #221,680

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 5:06:48 PM · Difficulty 9.9396 · 6,616,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4238984ea189f0f07138c9b0c451f697e73d57834d1114d891f4e3a1f6cd50c1

View on Chainz ↗

Height

#221,680

Difficulty

9.939574

Transactions

Size

1.58 KB

Version

Bits

09f087ee

Nonce

18,211

Timestamp

10/21/2013, 5:06:48 PM

Confirmations

6,616,101

Mined by

⛏️ aRe_AJhUq5LBVPv9saRZxaTzc7n48ikgcEVbqS

Merkle Root

2bcc8a39a0397fb1b4632a35f8835a7637239fba1d8fb2046da26c90bd077d9c

Transactions (1)

Coinbase2bcc8a39a0397f…a26c90bd077d9c

1 in → 43 out10.0900 XPM1.49 KB

AJhUq5LB…kgcEVbqS AKXeSXzu…yeuNjvhB ARpndEmc…Hg792kEk ASQjQCtG…LMRQkLKB AcMPa5Yh…j5yHgkwm

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.

2.093 × 10⁹¹(92-digit number)

20933213951058779500…17603636440215069019

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

2.093 × 10⁹¹(92-digit number)

20933213951058779500…17603636440215069019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.093 × 10⁹¹(92-digit number)

20933213951058779500…17603636440215069021

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

4.186 × 10⁹¹(92-digit number)

41866427902117559001…35207272880430138039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.186 × 10⁹¹(92-digit number)

41866427902117559001…35207272880430138041

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

8.373 × 10⁹¹(92-digit number)

83732855804235118002…70414545760860276079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.373 × 10⁹¹(92-digit number)

83732855804235118002…70414545760860276081

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

1.674 × 10⁹²(93-digit number)

16746571160847023600…40829091521720552159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.674 × 10⁹²(93-digit number)

16746571160847023600…40829091521720552161

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

3.349 × 10⁹²(93-digit number)

33493142321694047200…81658183043441104319

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 #221,680

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