Block #3,682,071

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2020, 11:31:28 AM · Difficulty 10.8782 · 3,161,146 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9958b8993e228f81b9bee88fc15da0008ae84e9bd82727371f4373a7d1b4c046

View on Chainz ↗

Height

#3,682,071

Difficulty

10.878191

Transactions

Size

7.52 KB

Version

Bits

0ae0d121

Nonce

695,407,137

Timestamp

5/12/2020, 11:31:28 AM

Confirmations

3,161,146

Mined by

⛏️ 8ASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

17ef59fe171f69d7b3c8a7e734a93972597e27a2b200e719b04b7a02a4fe0732

Transactions (5)

Coinbasefcbd59327a2c0a…9763c7be73287a

1 in → 1 out8.5400 XPM110 B

ASiq2qtK…VMhmk7yL

8a809f7dddc7a7…1bef8371c5fadc

60 in → 2 out505.7300 XPM6.76 KB

Ab5fFXVt…EC9k8a2d ASiq2qtK…VMhmk7yL

da7d69d7c5d58b…62e61df98bf73f

1 in → 2 out8.4200 XPM192 B

AZPRyPuB…ANsY2r6x ASiq2qtK…VMhmk7yL

d428234ea9a5a1…96db5ab806efed

1 in → 2 out8.4200 XPM192 B

ALxskxzJ…mwRWwWjn ASiq2qtK…VMhmk7yL

002b7cf255ebbf…dc89dd7d24e0d0

1 in → 2 out8.4200 XPM192 B

Ae9hKE3m…c55hrN2Y ASiq2qtK…VMhmk7yL

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.

9.740 × 10⁹³(94-digit number)

97400535968095320356…52307486836798794559

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

9.740 × 10⁹³(94-digit number)

97400535968095320356…52307486836798794559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.740 × 10⁹³(94-digit number)

97400535968095320356…52307486836798794561

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

1.948 × 10⁹⁴(95-digit number)

19480107193619064071…04614973673597589119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.948 × 10⁹⁴(95-digit number)

19480107193619064071…04614973673597589121

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

3.896 × 10⁹⁴(95-digit number)

38960214387238128142…09229947347195178239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.896 × 10⁹⁴(95-digit number)

38960214387238128142…09229947347195178241

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

7.792 × 10⁹⁴(95-digit number)

77920428774476256284…18459894694390356479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.792 × 10⁹⁴(95-digit number)

77920428774476256284…18459894694390356481

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

1.558 × 10⁹⁵(96-digit number)

15584085754895251256…36919789388780712959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.558 × 10⁹⁵(96-digit number)

15584085754895251256…36919789388780712961

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 #3,682,071

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