Block #3,506,476

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2020, 8:19:28 AM · Difficulty 10.9307 · 3,310,215 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

116eba8658e41e935076c37f5bdf072cbff20dfc20b35d6873eb1a08d9174d5b

View on Chainz ↗

Height

#3,506,476

Difficulty

10.930657

Transactions

Size

575 B

Version

Bits

0aee3f84

Nonce

347,645,607

Timestamp

1/9/2020, 8:19:28 AM

Confirmations

3,310,215

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

86af143543377d921c02645837ba09828fe5f35421c677431fb67cd56115e627

Transactions (2)

Coinbase637495bcf87b08…ccbbec6f09e2c8

1 in → 1 out8.3700 XPM109 B

ASiq2qtK…VMhmk7yL

92ec66ee4bad88…9c7253f0c1908b

2 in → 2 out7.9900 XPM374 B

ATzMJ1Dj…AZtUzrC5 AemG9P5h…FswX7gM3

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.

2.817 × 10⁹⁸(99-digit number)

28173495441989108109…33985076483474472959

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

2.817 × 10⁹⁸(99-digit number)

28173495441989108109…33985076483474472959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.817 × 10⁹⁸(99-digit number)

28173495441989108109…33985076483474472961

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

5.634 × 10⁹⁸(99-digit number)

56346990883978216219…67970152966948945919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.634 × 10⁹⁸(99-digit number)

56346990883978216219…67970152966948945921

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

1.126 × 10⁹⁹(100-digit number)

11269398176795643243…35940305933897891839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.126 × 10⁹⁹(100-digit number)

11269398176795643243…35940305933897891841

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

2.253 × 10⁹⁹(100-digit number)

22538796353591286487…71880611867795783679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.253 × 10⁹⁹(100-digit number)

22538796353591286487…71880611867795783681

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

4.507 × 10⁹⁹(100-digit number)

45077592707182572975…43761223735591567359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.507 × 10⁹⁹(100-digit number)

45077592707182572975…43761223735591567361

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 #3,506,476

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