Block #220,056

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 7:47:18 PM · Difficulty 9.9352 · 6,586,430 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1459d37a098ff79682e3e791ed2849b5771bc97a6f6f104eed39a4669c187de4

View on Chainz ↗

Height

#220,056

Difficulty

9.935200

Transactions

Size

2.16 KB

Version

Bits

09ef6942

Nonce

84,435

Timestamp

10/20/2013, 7:47:18 PM

Confirmations

6,586,430

Mined by

⛏️ Rd3ANuKx9Kemb4q2j6b7vjmfuKrAuwm7nrBRq

Merkle Root

1c48b5f0426b089c0bd5fa0fe25eb8b24990923ab5c8ce0189c07734a8b0df68

Transactions (2)

Coinbase54c9ca9a37e2f6…61ca97db8d5df8

1 in → 37 out10.1000 XPM1.29 KB

ANuKx9Ke…wm7nrBRq AbeUZSvK…ijGzuyjz ANxERLYc…v7fC1vqc AKXeSXzu…yeuNjvhB AdnG9gQ7…N9B7mA2p

ef1d975043cf42…fed1e81208dd8d

4 in → 10 out40.5800 XPM805 B

AbuU1HhS…JPwsJEbB ALhiG8Wa…tcZGAG9C AbMXywDa…iBhmMkLU AddYPtQ7…r1XeEMSA AKyT5sag…P1gmPYoR

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.

1.407 × 10⁹⁶(97-digit number)

14077564405233661494…55843246513854707199

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

1.407 × 10⁹⁶(97-digit number)

14077564405233661494…55843246513854707199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.407 × 10⁹⁶(97-digit number)

14077564405233661494…55843246513854707201

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

2.815 × 10⁹⁶(97-digit number)

28155128810467322988…11686493027709414399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.815 × 10⁹⁶(97-digit number)

28155128810467322988…11686493027709414401

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

5.631 × 10⁹⁶(97-digit number)

56310257620934645977…23372986055418828799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.631 × 10⁹⁶(97-digit number)

56310257620934645977…23372986055418828801

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

1.126 × 10⁹⁷(98-digit number)

11262051524186929195…46745972110837657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.126 × 10⁹⁷(98-digit number)

11262051524186929195…46745972110837657601

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

2.252 × 10⁹⁷(98-digit number)

22524103048373858390…93491944221675315199

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 #220,056

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