Block #1,506,092

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/21/2016, 9:09:48 AM · Difficulty 10.6354 · 5,306,144 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc3fb11885f9ab5f3a46a6bd053794bd59f8761a41e307241e3655b0a39812c9

View on Chainz ↗

Height

#1,506,092

Difficulty

10.635351

Transactions

Size

1.13 KB

Version

Bits

0aa2a659

Nonce

728,697,637

Timestamp

3/21/2016, 9:09:48 AM

Confirmations

5,306,144

Mined by

⛏️ P2SHARsEmgKst9i8QzhpymP38CUpPkPL95gVmG

Merkle Root

19d4caae9310c1bdf357c3219a17d13e3f2fb59cf8ac4cac7c8536ae44eb5a16

Transactions (3)

Coinbasea8c685215521cd…ab02cdc49f865a

1 in → 1 out8.8500 XPM109 B

ARsEmgKs…PL95gVmG

b6f4d22c6b3528…a5fcf2c4ef8670

1 in → 2 out999.9900 XPM227 B

AM4pDoh2…2vkqeuS3 AKwEDgpL…4XxRWbCa

e2a2206b4a7ae7…fe9c403705a853

1 in → 17 out207.1122 XPM736 B

AFxxYVtW…76zFbjN1 AKBNwFgR…tEXZybXv AP36U8B9…avBYEdr9 AGanE1Wb…jpZARgZm APM8ptnq…r5hdjtZo

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.

2.689 × 10⁹⁴(95-digit number)

26890822494512200491…93488868438096783359

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

2.689 × 10⁹⁴(95-digit number)

26890822494512200491…93488868438096783359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.689 × 10⁹⁴(95-digit number)

26890822494512200491…93488868438096783361

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

5.378 × 10⁹⁴(95-digit number)

53781644989024400983…86977736876193566719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.378 × 10⁹⁴(95-digit number)

53781644989024400983…86977736876193566721

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

1.075 × 10⁹⁵(96-digit number)

10756328997804880196…73955473752387133439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.075 × 10⁹⁵(96-digit number)

10756328997804880196…73955473752387133441

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

2.151 × 10⁹⁵(96-digit number)

21512657995609760393…47910947504774266879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.151 × 10⁹⁵(96-digit number)

21512657995609760393…47910947504774266881

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

4.302 × 10⁹⁵(96-digit number)

43025315991219520786…95821895009548533759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.302 × 10⁹⁵(96-digit number)

43025315991219520786…95821895009548533761

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

8.605 × 10⁹⁵(96-digit number)

86050631982439041573…91643790019097067519

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 #1,506,092

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