Block #3,503,464

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2020, 5:56:13 AM · Difficulty 10.9307 · 3,323,672 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d888c01709a6bb5f8da9bc7b3384e0d850736e28fd57dbd7ea773583cf286f2b

View on Chainz ↗

Height

#3,503,464

Difficulty

10.930711

Transactions

Size

7.47 KB

Version

Bits

0aee4313

Nonce

276,375,650

Timestamp

1/7/2020, 5:56:13 AM

Confirmations

3,323,672

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMz Visit pool ↗

Merkle Root

3cf24e1570b198823b443150749995f9e268898ae3aa3194b9ef842bbb1c4f04

Transactions (2)

Coinbased266ccad768f2b…7d95d3521293d8

1 in → 1 out8.4400 XPM110 B

AXfJqzUb…HXeXmjMz

85786e97f72a28…639625d45f6a87

50 in → 1 out499.9200 XPM7.28 KB

ALcTQaSP…1C5Yf2Zi

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.

2.201 × 10⁹⁶(97-digit number)

22012113331900702827…94656053686270914559

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

2.201 × 10⁹⁶(97-digit number)

22012113331900702827…94656053686270914559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.201 × 10⁹⁶(97-digit number)

22012113331900702827…94656053686270914561

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

4.402 × 10⁹⁶(97-digit number)

44024226663801405655…89312107372541829119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.402 × 10⁹⁶(97-digit number)

44024226663801405655…89312107372541829121

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

8.804 × 10⁹⁶(97-digit number)

88048453327602811310…78624214745083658239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.804 × 10⁹⁶(97-digit number)

88048453327602811310…78624214745083658241

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

1.760 × 10⁹⁷(98-digit number)

17609690665520562262…57248429490167316479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.760 × 10⁹⁷(98-digit number)

17609690665520562262…57248429490167316481

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

3.521 × 10⁹⁷(98-digit number)

35219381331041124524…14496858980334632959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.521 × 10⁹⁷(98-digit number)

35219381331041124524…14496858980334632961

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 #3,503,464

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