Block #1,465,156

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/20/2016, 4:04:20 AM · Difficulty 10.7798 · 5,352,809 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b87a128fcaa7d3ce12a4fdf94ab0189aeceeacc5e93b4770c97885ad557f2335

View on Chainz ↗

Height

#1,465,156

Difficulty

10.779759

Transactions

Size

800 B

Version

Bits

0ac79e50

Nonce

1,300,635,760

Timestamp

2/20/2016, 4:04:20 AM

Confirmations

5,352,809

Mined by

⛏️ P2SHAJwyFNk2No8ad9Th8yUd1xjLjroKvPFD8i

Merkle Root

5e336f4cf72f894acb6845b86ce351c7b3e888d3183cc7fc7164a79d829fc5c1

Transactions (2)

Coinbase9bee565e7d8567…5cd98176cc03a7

1 in → 1 out8.6000 XPM110 B

AJwyFNk2…oKvPFD8i

c4029ba3d08138…4935781225701f

1 in → 13 out151.0890 XPM600 B

AJTvZHyH…x1hwUE55 AZzkdGE9…DsnGusqd ARkRc4cS…NYv7PBbJ AMznJws3…LpVbLJfo AWL2maao…gT97jevq

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.

1.746 × 10⁹⁴(95-digit number)

17462862805309374050…10942268077989701759

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

1.746 × 10⁹⁴(95-digit number)

17462862805309374050…10942268077989701759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.746 × 10⁹⁴(95-digit number)

17462862805309374050…10942268077989701761

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

3.492 × 10⁹⁴(95-digit number)

34925725610618748101…21884536155979403519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.492 × 10⁹⁴(95-digit number)

34925725610618748101…21884536155979403521

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

6.985 × 10⁹⁴(95-digit number)

69851451221237496203…43769072311958807039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.985 × 10⁹⁴(95-digit number)

69851451221237496203…43769072311958807041

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

1.397 × 10⁹⁵(96-digit number)

13970290244247499240…87538144623917614079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.397 × 10⁹⁵(96-digit number)

13970290244247499240…87538144623917614081

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

2.794 × 10⁹⁵(96-digit number)

27940580488494998481…75076289247835228159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.794 × 10⁹⁵(96-digit number)

27940580488494998481…75076289247835228161

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 #1,465,156

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