Block #1,281,649

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/14/2015, 11:40:15 AM · Difficulty 10.8401 · 5,526,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

355f1833c39cf9d54dcd88953ecacb1bca81602225088f9108c7bad8ac6c224e

View on Chainz ↗

Height

#1,281,649

Difficulty

10.840148

Transactions

Size

1.01 KB

Version

Bits

0ad713eb

Nonce

748,017,156

Timestamp

10/14/2015, 11:40:15 AM

Confirmations

5,526,511

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

257a21b4c5996dd4c90dc5f6e3d16edcf63162d809fc3b9addf226642a475eef

Transactions (4)

Coinbasec80abaeda91a7f…f5236d7bba7d5e

1 in → 1 out8.5300 XPM116 B

AJCEY9yy…tg97E6zm

29e5c9b79d74f2…3389fa718f65cb

2 in → 2 out14.1631 XPM373 B

Aa7M1w3S…hGgKV6xq AbMeRh4h…e6PYFRf2

370c0b80e233d3…9605ed7d53925e

1 in → 2 out8.5000 XPM226 B

ASiAqfbQ…51m4pxCB ANbiQjey…vAcn3WWv

a2c31e09549c50…eddc852c31bfc7

1 in → 2 out8.5000 XPM226 B

ASd1kwRW…3FxG5vC2 AT3PgqMv…zoC2druJ

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.

1.861 × 10⁹⁴(95-digit number)

18617517928087521818…78328718886835480199

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

1.861 × 10⁹⁴(95-digit number)

18617517928087521818…78328718886835480199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.861 × 10⁹⁴(95-digit number)

18617517928087521818…78328718886835480201

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

3.723 × 10⁹⁴(95-digit number)

37235035856175043637…56657437773670960399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.723 × 10⁹⁴(95-digit number)

37235035856175043637…56657437773670960401

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

7.447 × 10⁹⁴(95-digit number)

74470071712350087275…13314875547341920799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.447 × 10⁹⁴(95-digit number)

74470071712350087275…13314875547341920801

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

1.489 × 10⁹⁵(96-digit number)

14894014342470017455…26629751094683841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.489 × 10⁹⁵(96-digit number)

14894014342470017455…26629751094683841601

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

2.978 × 10⁹⁵(96-digit number)

29788028684940034910…53259502189367683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.978 × 10⁹⁵(96-digit number)

29788028684940034910…53259502189367683201

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 #1,281,649

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