Block #1,504,287

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2016, 11:15:53 PM · Difficulty 10.6513 · 5,307,841 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18048b90a3789e770648b1ecc5c9f74f6295b749313f0b11ac4d15c71a691754

View on Chainz ↗

Height

#1,504,287

Difficulty

10.651318

Transactions

Size

7.87 KB

Version

Bits

0aa6bcc7

Nonce

1,957,455,927

Timestamp

3/19/2016, 11:15:53 PM

Confirmations

5,307,841

Mined by

⛏️ P2SHAR9NSd2KRJs2wXv1FZQMgMRRDqyUsZy6Sq

Merkle Root

6d8dd6e130e828ff3f6bf0614a38dee43fa950a1b30d03505f24affc491fcd50

Transactions (5)

Coinbasefb0ff81f548112…8d8a82e653cb35

1 in → 1 out8.8900 XPM109 B

AR9NSd2K…yUsZy6Sq

13e61ba47eae5b…5ff9f7abf52f78

1 in → 51 out94.9451 XPM1.85 KB

AKmAS4bM…Rs1nSAUa AeMqkGnU…nGL6UHUz APPCxuNL…YTNNV3LY AJtNCstA…xiZBp8M1 AHTfCLbC…hUobwYqC

4527c257903a04…a6648208f88325

1 in → 51 out37.1968 XPM1.85 KB

ATQ2RfSs…yao2HZMj ARgHSVJU…1Hu8Gr8P AcfKLd8n…HqH9LZHu AM2zC8oK…UwE5bNAg Abqfb2c3…fh7Zy9P3

bf022850331fbc…b753b37514c785

3 in → 51 out6.6106 XPM2.14 KB

AZ3cZHxS…1qdoLqba AddUSmgB…nsNX1H2E Acr54Uhg…FeYtSbEq AHAVPAh8…qysfyzBD AFxxYVtW…76zFbjN1

8dde946b985bc9…aaa1c0e78440fe

1 in → 51 out2.4322 XPM1.85 KB

AH6at3Eu…7gsfysyP ALWcRwqS…KAy9F9nQ AdcFFzNr…XW2Q2UXo ARK2bLog…8tXC5W82 AYaBwRDh…KNQDXY3B

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.

9.003 × 10⁹⁴(95-digit number)

90030025511315893466…75598766699646274559

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

9.003 × 10⁹⁴(95-digit number)

90030025511315893466…75598766699646274559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.003 × 10⁹⁴(95-digit number)

90030025511315893466…75598766699646274561

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

1.800 × 10⁹⁵(96-digit number)

18006005102263178693…51197533399292549119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.800 × 10⁹⁵(96-digit number)

18006005102263178693…51197533399292549121

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

3.601 × 10⁹⁵(96-digit number)

36012010204526357386…02395066798585098239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.601 × 10⁹⁵(96-digit number)

36012010204526357386…02395066798585098241

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

7.202 × 10⁹⁵(96-digit number)

72024020409052714773…04790133597170196479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.202 × 10⁹⁵(96-digit number)

72024020409052714773…04790133597170196481

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

1.440 × 10⁹⁶(97-digit number)

14404804081810542954…09580267194340392959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.440 × 10⁹⁶(97-digit number)

14404804081810542954…09580267194340392961

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 #1,504,287

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