Block #2,642,865

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 9:37:11 PM · Difficulty 11.6662 · 4,188,019 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a61dd1f353b9abb5899c141265e90bb5f70e208418f34e62aa9dab887317f26a

View on Chainz ↗

Height

#2,642,865

Difficulty

11.666193

Transactions

Size

1.51 KB

Version

Bits

0baa8b9c

Nonce

895,977,583

Timestamp

5/1/2018, 9:37:11 PM

Confirmations

4,188,019

Mined by

⛏️ P2SHASkbGFGb2wYw4pAxouK7KEmusJAiV6sLLb

Merkle Root

86e3532a267819c1364e3c1f1cabec7ead8ea6de8a5c188433b92100268603c3

Transactions (5)

Coinbase0d9872b1d81622…acbf866a491044

1 in → 1 out7.3800 XPM110 B

ASkbGFGb…AiV6sLLb

3dc025f3077ec9…6ea4abfc551c37

2 in → 3 out276.3103 XPM407 B

AeE8jzQC…xaMsk2EK AJrF4w4U…GvC5YqUn AVnh7R3U…Ksy2vvj3

f5cb16018d1a68…42dbe423107ada

3 in → 2 out10.4696 XPM486 B

ALdjb6um…WuaWJUSs ANycnEPQ…gFPEhD1u

bbd2ddc6e5043c…4940ddf0dbb36b

1 in → 2 out5.3330 XPM227 B

AN57RYsV…BatcYF72 AJ64A3i2…UjNpZxDY

448b899097300f…f1dd74b680a796

1 in → 2 out1.2273 XPM227 B

AUNzLbFq…3g9bqzhn AMFxoiZV…2UX5WRMn

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.

1.077 × 10⁹⁸(99-digit number)

10777398299993254295…43422450338136555519

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

1.077 × 10⁹⁸(99-digit number)

10777398299993254295…43422450338136555519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.077 × 10⁹⁸(99-digit number)

10777398299993254295…43422450338136555521

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

2.155 × 10⁹⁸(99-digit number)

21554796599986508590…86844900676273111039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.155 × 10⁹⁸(99-digit number)

21554796599986508590…86844900676273111041

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

4.310 × 10⁹⁸(99-digit number)

43109593199973017181…73689801352546222079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.310 × 10⁹⁸(99-digit number)

43109593199973017181…73689801352546222081

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

8.621 × 10⁹⁸(99-digit number)

86219186399946034363…47379602705092444159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.621 × 10⁹⁸(99-digit number)

86219186399946034363…47379602705092444161

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

1.724 × 10⁹⁹(100-digit number)

17243837279989206872…94759205410184888319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.724 × 10⁹⁹(100-digit number)

17243837279989206872…94759205410184888321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.448 × 10⁹⁹(100-digit number)

34487674559978413745…89518410820369776639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,642,865

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