Block #1,534,484

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 6:47:38 AM · Difficulty 10.6171 · 5,283,004 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7af7887676629fb427ea8bf36475b64546929561cb24874d1e17792c2c14769f

View on Chainz ↗

Height

#1,534,484

Difficulty

10.617144

Transactions

Size

15.02 KB

Version

Bits

0a9dfd27

Nonce

369,696,787

Timestamp

4/10/2016, 6:47:38 AM

Confirmations

5,283,004

Mined by

⛏️ P2SHAJgB789tqLAoWdwNDCWJx3Y5n6Yn2rSakp

Merkle Root

deff684349cd84a9d9bf59aff05eb554253b586b93a86f326ab6327e1e767d42

Transactions (3)

Coinbase92892d6b631ff3…1b7e0fd663c4a5

1 in → 1 out9.0200 XPM109 B

AJgB789t…Yn2rSakp

a15606cd950526…dda8f23c103c05

51 in → 1 out2749.0355 XPM7.41 KB

ASa7dFFJ…TGxdsj1E

8c1bff1762f5da…003b1ddd0ce849

51 in → 1 out1119.3915 XPM7.42 KB

ATtgPoCh…RF9bZfss

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.

7.682 × 10⁹⁷(98-digit number)

76823232293213787346…55482502876902195199

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

7.682 × 10⁹⁷(98-digit number)

76823232293213787346…55482502876902195199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.682 × 10⁹⁷(98-digit number)

76823232293213787346…55482502876902195201

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

1.536 × 10⁹⁸(99-digit number)

15364646458642757469…10965005753804390399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.536 × 10⁹⁸(99-digit number)

15364646458642757469…10965005753804390401

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

3.072 × 10⁹⁸(99-digit number)

30729292917285514938…21930011507608780799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.072 × 10⁹⁸(99-digit number)

30729292917285514938…21930011507608780801

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

6.145 × 10⁹⁸(99-digit number)

61458585834571029876…43860023015217561599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.145 × 10⁹⁸(99-digit number)

61458585834571029876…43860023015217561601

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

1.229 × 10⁹⁹(100-digit number)

12291717166914205975…87720046030435123199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.229 × 10⁹⁹(100-digit number)

12291717166914205975…87720046030435123201

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 #1,534,484

Cookie Preferences