Block #1,571,816

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/4/2016, 11:04:13 PM · Difficulty 10.7331 · 5,260,743 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

740852dd0948cf72d201b0010e47b815d232036540de1ea037d12d6da30b1cfc

View on Chainz ↗

Height

#1,571,816

Difficulty

10.733115

Transactions

Size

577 B

Version

Bits

0abbad74

Nonce

175,007,922

Timestamp

5/4/2016, 11:04:13 PM

Confirmations

5,260,743

Mined by

⛏️ P2SHAVmPmJ5Jvqj7ztzQDKNKjvW8SNpUafmk58

Merkle Root

6c424e951632cc007e47b7941733c91f4f8ad4544bce162a1e591f80ea599fcb

Transactions (2)

Coinbase29b40a53fcf9ad…4f80419780a597

1 in → 1 out8.6800 XPM110 B

AVmPmJ5J…pUafmk58

5c2cda0d988feb…197e102881734d

2 in → 2 out44.2709 XPM375 B

AcPsbh66…WyGDfnCd ARcqYbt6…XhDgexUG

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.

3.310 × 10⁹⁸(99-digit number)

33101431915556504371…35873344384666828799

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

3.310 × 10⁹⁸(99-digit number)

33101431915556504371…35873344384666828799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.310 × 10⁹⁸(99-digit number)

33101431915556504371…35873344384666828801

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

6.620 × 10⁹⁸(99-digit number)

66202863831113008742…71746688769333657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.620 × 10⁹⁸(99-digit number)

66202863831113008742…71746688769333657601

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

1.324 × 10⁹⁹(100-digit number)

13240572766222601748…43493377538667315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.324 × 10⁹⁹(100-digit number)

13240572766222601748…43493377538667315201

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

2.648 × 10⁹⁹(100-digit number)

26481145532445203497…86986755077334630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.648 × 10⁹⁹(100-digit number)

26481145532445203497…86986755077334630401

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

5.296 × 10⁹⁹(100-digit number)

52962291064890406994…73973510154669260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.296 × 10⁹⁹(100-digit number)

52962291064890406994…73973510154669260801

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 #1,571,816

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