Block #363,970

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 6:28:31 PM · Difficulty 10.4184 · 6,462,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1318f24c9baa7ac78667108bb690ef6e6ed0d42cbd5276a34c469dc26f37179

View on Chainz ↗

Height

#363,970

Difficulty

10.418361

Transactions

Size

1.08 KB

Version

Bits

0a6b19b6

Nonce

13,537

Timestamp

1/17/2014, 6:28:31 PM

Confirmations

6,462,464

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cfcdc0e63e792af74a411ed710b073475a04198efc9ac655c87291fa168df038

Transactions (5)

Coinbase49e76bd8616912…90cba557768ecb

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

b8ec09504d74ca…eecfbc24c9d918

1 in → 2 out7.1784 XPM226 B

ATYTKh4h…jNN3nAdZ AHg1i3CQ…jcKctFwV

cf4e475f4af826…24ef3cca51ee75

1 in → 2 out3.1478 XPM225 B

ATWTFaHp…PqMsojuH AGAa9dwm…zyz93b4i

df46fa7372536e…15a91325be9d3a

1 in → 2 out5.0554 XPM226 B

AbHXKZhu…1udzBYgQ AeXC7FDN…TqagBb44

41d44fc78d4712…e5650720c7a515

1 in → 2 out3.0781 XPM227 B

AN3EzRAi…ve71VGRy APWKxwCK…wU1BQKNQ

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.

1.698 × 10⁹⁷(98-digit number)

16981453245735319068…62283735124443636959

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

1.698 × 10⁹⁷(98-digit number)

16981453245735319068…62283735124443636959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.698 × 10⁹⁷(98-digit number)

16981453245735319068…62283735124443636961

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

3.396 × 10⁹⁷(98-digit number)

33962906491470638137…24567470248887273919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.396 × 10⁹⁷(98-digit number)

33962906491470638137…24567470248887273921

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

6.792 × 10⁹⁷(98-digit number)

67925812982941276274…49134940497774547839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.792 × 10⁹⁷(98-digit number)

67925812982941276274…49134940497774547841

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

1.358 × 10⁹⁸(99-digit number)

13585162596588255254…98269880995549095679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.358 × 10⁹⁸(99-digit number)

13585162596588255254…98269880995549095681

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

2.717 × 10⁹⁸(99-digit number)

27170325193176510509…96539761991098191359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.717 × 10⁹⁸(99-digit number)

27170325193176510509…96539761991098191361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #363,970

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