Block #1,359,787

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2015, 7:49:26 PM · Difficulty 10.8394 · 5,431,967 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f45338707fd6c13feaeb134c5b3bc634cd97dcc91d3a8b390423317c7db8f4be

View on Chainz ↗

Height

#1,359,787

Difficulty

10.839422

Transactions

Size

798 B

Version

Bits

0ad6e461

Nonce

151,254,474

Timestamp

12/7/2015, 7:49:26 PM

Confirmations

5,431,967

Merkle Root

f18337962f62be7ee19d6330e595dc151ac9a15ccfb2c2d80a261c7d09200f2f

Transactions (3)

Coinbase12e7f63fc8d9fb…f4dcbab66dd18a

1 in → 1 out8.5200 XPM109 B

ATVPZcPM…3MHKbcKN

ae7a3f4897526c…5003b23ac4a792

2 in → 2 out10.1962 XPM374 B

ALFt3VUi…dXftBRGs AJRwGPSP…QDRWdi2B

8fda15b18f937e…80a5ffc79b280f

1 in → 2 out6.1773 XPM225 B

AcuM7XiJ…5uND8Jce AeVMeHGy…axugkQ18

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.

1.053 × 10⁹⁵(96-digit number)

10534759892679723442…03363358122131925599

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

1.053 × 10⁹⁵(96-digit number)

10534759892679723442…03363358122131925599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.053 × 10⁹⁵(96-digit number)

10534759892679723442…03363358122131925601

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

2.106 × 10⁹⁵(96-digit number)

21069519785359446885…06726716244263851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.106 × 10⁹⁵(96-digit number)

21069519785359446885…06726716244263851201

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

4.213 × 10⁹⁵(96-digit number)

42139039570718893770…13453432488527702399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.213 × 10⁹⁵(96-digit number)

42139039570718893770…13453432488527702401

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

8.427 × 10⁹⁵(96-digit number)

84278079141437787540…26906864977055404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.427 × 10⁹⁵(96-digit number)

84278079141437787540…26906864977055404801

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

1.685 × 10⁹⁶(97-digit number)

16855615828287557508…53813729954110809599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.685 × 10⁹⁶(97-digit number)

16855615828287557508…53813729954110809601

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