Block #4,062,916

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2021, 9:08:54 PM · Difficulty 10.8053 · 2,754,253 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

778a7a635a5681a96a990b01793a62eadb2aecdccc9a048874ce9069c11f2bae

View on Chainz ↗

Height

#4,062,916

Difficulty

10.805287

Transactions

Size

1.18 KB

Version

Bits

0ace2743

Nonce

1,356,080,720

Timestamp

2/2/2021, 9:08:54 PM

Confirmations

2,754,253

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

670e291abc20d2a73311b831b6bd19f5efbc3981c2365e1157758e55b26f5b8b

Transactions (3)

Coinbase43121cbaa87aeb…dee5891ff948b7

1 in → 1 out8.5700 XPM110 B

ASiq2qtK…VMhmk7yL

a00d3b5eeea5cc…a8dec53ce15cd3

5 in → 2 out10.8428 XPM785 B

ASiq2qtK…VMhmk7yL Ab6uYUja…EseWVMwa

261691782c5577…c5406900037bd6

1 in → 2 out4.4146 XPM226 B

AQvoeGK8…yd72tRVu 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.

1.329 × 10⁹⁸(99-digit number)

13294950593714611470…02699256986695434239

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

1.329 × 10⁹⁸(99-digit number)

13294950593714611470…02699256986695434239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.329 × 10⁹⁸(99-digit number)

13294950593714611470…02699256986695434241

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

2.658 × 10⁹⁸(99-digit number)

26589901187429222941…05398513973390868479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.658 × 10⁹⁸(99-digit number)

26589901187429222941…05398513973390868481

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

5.317 × 10⁹⁸(99-digit number)

53179802374858445882…10797027946781736959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.317 × 10⁹⁸(99-digit number)

53179802374858445882…10797027946781736961

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

1.063 × 10⁹⁹(100-digit number)

10635960474971689176…21594055893563473919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.063 × 10⁹⁹(100-digit number)

10635960474971689176…21594055893563473921

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

2.127 × 10⁹⁹(100-digit number)

21271920949943378353…43188111787126947839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.127 × 10⁹⁹(100-digit number)

21271920949943378353…43188111787126947841

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 #4,062,916

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