Block #220,461

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 1:05:48 AM · Difficulty 9.9364 · 6,589,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d77dfab9dc0b4c114bd462f97084f7075a76f1e26774f892722711dcaffdb65c

View on Chainz ↗

Height

#220,461

Difficulty

9.936353

Transactions

Size

1.21 KB

Version

Bits

09efb4da

Nonce

43,490

Timestamp

10/21/2013, 1:05:48 AM

Confirmations

6,589,417

Mined by

⛏️ P2SHAUPANJpSzZPbmLrNYMGUkQHJhiEkxNC6Ud

Merkle Root

7390a0ce27cf0051cf7144685645535c05797bdf733f1560143cc75b9c3c205e

Transactions (3)

Coinbase27797938b14437…c09cf61c0ba3c5

1 in → 1 out10.1300 XPM110 B

AUPANJpS…EkxNC6Ud

84739f4d8ee4a2…e2b5b9eb23d770

3 in → 2 out30.3800 XPM521 B

AN5XB15f…BKxb7cz3 AZoTowvW…KJoS4PJA

5d1b998361a2a6…16b4898f90ac6d

3 in → 2 out6.5050 XPM519 B

AKjK7mFq…Af8yTmrA AaiKMEh2…PPCs1M8h

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.

3.309 × 10⁹⁷(98-digit number)

33098515276131136070…73179744116079779839

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

3.309 × 10⁹⁷(98-digit number)

33098515276131136070…73179744116079779839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.309 × 10⁹⁷(98-digit number)

33098515276131136070…73179744116079779841

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

6.619 × 10⁹⁷(98-digit number)

66197030552262272141…46359488232159559679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.619 × 10⁹⁷(98-digit number)

66197030552262272141…46359488232159559681

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

1.323 × 10⁹⁸(99-digit number)

13239406110452454428…92718976464319119359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.323 × 10⁹⁸(99-digit number)

13239406110452454428…92718976464319119361

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

2.647 × 10⁹⁸(99-digit number)

26478812220904908856…85437952928638238719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.647 × 10⁹⁸(99-digit number)

26478812220904908856…85437952928638238721

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

5.295 × 10⁹⁸(99-digit number)

52957624441809817713…70875905857276477439

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 #220,461

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