Block #3,971,701

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2020, 10:32:01 AM · Difficulty 10.8551 · 2,840,197 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

61f1c9a5b4ce332dcab6857c13c68180a16f4d0fce366889b4a8004a016f6f45

View on Chainz ↗

Height

#3,971,701

Difficulty

10.855079

Transactions

Size

1.91 KB

Version

Bits

0adae670

Nonce

1,026,336,473

Timestamp

11/30/2020, 10:32:01 AM

Confirmations

2,840,197

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

67100365fab63f2533d04625657fffe40f263d09bc274fe546a8792f4099d88d

Transactions (3)

Coinbaseea5a3bd522fe8b…15f10bf3fc69b2

1 in → 1 out8.5000 XPM110 B

ASiq2qtK…VMhmk7yL

c1e7090cf96100…2966ab6bfbe24d

12 in → 2 out101.4900 XPM1.41 KB

AXMsS7rS…QVJwPNhf ASiq2qtK…VMhmk7yL

30e3049b232cfa…6a89033f8ca2c3

2 in → 2 out16.9000 XPM306 B

ASiq2qtK…VMhmk7yL Ab6uYUja…EseWVMwa

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.

1.665 × 10⁹⁶(97-digit number)

16654877923462111358…50750015898744586239

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

1.665 × 10⁹⁶(97-digit number)

16654877923462111358…50750015898744586239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.665 × 10⁹⁶(97-digit number)

16654877923462111358…50750015898744586241

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

3.330 × 10⁹⁶(97-digit number)

33309755846924222716…01500031797489172479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.330 × 10⁹⁶(97-digit number)

33309755846924222716…01500031797489172481

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

6.661 × 10⁹⁶(97-digit number)

66619511693848445432…03000063594978344959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.661 × 10⁹⁶(97-digit number)

66619511693848445432…03000063594978344961

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

1.332 × 10⁹⁷(98-digit number)

13323902338769689086…06000127189956689919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.332 × 10⁹⁷(98-digit number)

13323902338769689086…06000127189956689921

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

2.664 × 10⁹⁷(98-digit number)

26647804677539378172…12000254379913379839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.664 × 10⁹⁷(98-digit number)

26647804677539378172…12000254379913379841

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 #3,971,701

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