Block #1,178,264

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/31/2015, 12:38:39 PM · Difficulty 10.9340 · 5,665,324 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9a5c8f13bffeaa62f233b2d00fb68ae48910604b5ed9a47f3a52ede6b040972

View on Chainz ↗

Height

#1,178,264

Difficulty

10.934029

Transactions

Size

433 B

Version

Bits

0aef1c88

Nonce

262,985,647

Timestamp

7/31/2015, 12:38:39 PM

Confirmations

5,665,324

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

136662a6b653c16928f3dbae6d9a280c749591fe6f8e3acfaa66670c3b895de7

Transactions (2)

Coinbase630f160b7aa431…fb9a14d9256110

1 in → 1 out8.3600 XPM116 B

AJCEY9yy…tg97E6zm

0ad7cbb8f6d846…72cbe0b94ca292

1 in → 2 out3768.6223 XPM226 B

APwiG1jQ…mkUcTowU AQ539rFh…XyFao7mE

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.

2.352 × 10⁹⁶(97-digit number)

23524981198092156512…54829066470191127039

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

2.352 × 10⁹⁶(97-digit number)

23524981198092156512…54829066470191127039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.352 × 10⁹⁶(97-digit number)

23524981198092156512…54829066470191127041

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

4.704 × 10⁹⁶(97-digit number)

47049962396184313025…09658132940382254079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.704 × 10⁹⁶(97-digit number)

47049962396184313025…09658132940382254081

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

9.409 × 10⁹⁶(97-digit number)

94099924792368626050…19316265880764508159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.409 × 10⁹⁶(97-digit number)

94099924792368626050…19316265880764508161

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

1.881 × 10⁹⁷(98-digit number)

18819984958473725210…38632531761529016319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.881 × 10⁹⁷(98-digit number)

18819984958473725210…38632531761529016321

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

3.763 × 10⁹⁷(98-digit number)

37639969916947450420…77265063523058032639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.763 × 10⁹⁷(98-digit number)

37639969916947450420…77265063523058032641

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 #1,178,264

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