Block #1,144,337

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/8/2015, 5:50:30 AM · Difficulty 10.9274 · 5,666,429 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6598330196fc41256e2803f32150477b970d8e33e935fbc214c57d26fed530cf

View on Chainz ↗

Height

#1,144,337

Difficulty

10.927371

Transactions

Size

2.01 KB

Version

Bits

0aed682e

Nonce

1,348,874,831

Timestamp

7/8/2015, 5:50:30 AM

Confirmations

5,666,429

Mined by

⛏️ P2SHAHxr8s87362mtzrjShN2rRynWkiWyBRNif

Merkle Root

701a978039d54034f81517743254bca060cd53d3e7dcfdba7c85b3659281b0c0

Transactions (2)

Coinbased5c13126e6be22…d7517918239fd7

1 in → 1 out8.4000 XPM110 B

AHxr8s87…iWyBRNif

71e3e770f558de…7553efac99e353

12 in → 2 out374.9564 XPM1.81 KB

AQST4WvS…2ZWCWtck AaxCzsay…bAqhqJEy

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.

1.531 × 10⁹⁷(98-digit number)

15319752286253507741…33060492809578577919

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

1.531 × 10⁹⁷(98-digit number)

15319752286253507741…33060492809578577919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.531 × 10⁹⁷(98-digit number)

15319752286253507741…33060492809578577921

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

3.063 × 10⁹⁷(98-digit number)

30639504572507015483…66120985619157155839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.063 × 10⁹⁷(98-digit number)

30639504572507015483…66120985619157155841

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

6.127 × 10⁹⁷(98-digit number)

61279009145014030966…32241971238314311679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.127 × 10⁹⁷(98-digit number)

61279009145014030966…32241971238314311681

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

1.225 × 10⁹⁸(99-digit number)

12255801829002806193…64483942476628623359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.225 × 10⁹⁸(99-digit number)

12255801829002806193…64483942476628623361

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

2.451 × 10⁹⁸(99-digit number)

24511603658005612386…28967884953257246719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.451 × 10⁹⁸(99-digit number)

24511603658005612386…28967884953257246721

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 #1,144,337

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