Block #493,395

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 4:26:56 PM · Difficulty 10.6994 · 6,309,659 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3687c796d492b144761f30de62bbdb90fdebec29cbbfc61f47ce46be17d3996

View on Chainz ↗

Height

#493,395

Difficulty

10.699447

Transactions

Size

1.07 KB

Version

Bits

0ab30eee

Nonce

64,460

Timestamp

4/15/2014, 4:26:56 PM

Confirmations

6,309,659

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5d2e455ba72eace594e17cde0f8b4c62795f6a0127125a928c5a937356092c77

Transactions (3)

Coinbase41056fab75de29…bbb52efe1fae50

1 in → 1 out8.7400 XPM116 B

AbwWkWZt…kawDhufa

60fe09fe41a0d3…a7700ed43a8887

3 in → 9 out26.3100 XPM658 B

AYmLcThu…bcDqL7gN ATXFZVYv…JduPzKNb ASTcaxJ4…gURy1LJz AdpsxmtJ…ZWfmvRK9 AXDEZh15…FbrAPGkC

a28c2aea5070a4…2d1bf6a1e61cae

1 in → 2 out4.9902 XPM226 B

AZB6zbiz…4EfgWFki AentXecu…Lyg7dBkG

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.

3.927 × 10⁹⁷(98-digit number)

39270831353780531134…03212579394044404399

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

3.927 × 10⁹⁷(98-digit number)

39270831353780531134…03212579394044404399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.927 × 10⁹⁷(98-digit number)

39270831353780531134…03212579394044404401

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

7.854 × 10⁹⁷(98-digit number)

78541662707561062269…06425158788088808799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.854 × 10⁹⁷(98-digit number)

78541662707561062269…06425158788088808801

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

1.570 × 10⁹⁸(99-digit number)

15708332541512212453…12850317576177617599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.570 × 10⁹⁸(99-digit number)

15708332541512212453…12850317576177617601

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

3.141 × 10⁹⁸(99-digit number)

31416665083024424907…25700635152355235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.141 × 10⁹⁸(99-digit number)

31416665083024424907…25700635152355235201

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

6.283 × 10⁹⁸(99-digit number)

62833330166048849815…51401270304710470399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.283 × 10⁹⁸(99-digit number)

62833330166048849815…51401270304710470401

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