Block #1,224,778

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/6/2015, 4:37:41 PM · Difficulty 10.7379 · 5,581,019 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9cbb32572d677abdd657d6148648fa78043cec12c5f257651ab8e8ca1a8d6daf

View on Chainz ↗

Height

#1,224,778

Difficulty

10.737903

Transactions

Size

882 B

Version

Bits

0abce73a

Nonce

1,310,828,541

Timestamp

9/6/2015, 4:37:41 PM

Confirmations

5,581,019

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

c44fe553bd89d4ae4d1a0105dbcbec90a73ed060dd363064e32316013c771d29

Transactions (4)

Coinbase3d2472907a5491…9d924884113709

1 in → 1 out8.6900 XPM116 B

AJCEY9yy…tg97E6zm

ae2551654c0fc4…ae1567fdf45663

1 in → 2 out5.4041 XPM225 B

AcQw6Sx1…vyP7zH6q AVnmjzK4…gEj3QBN2

5d73b09b8e3ed6…2880a82d91097a

1 in → 2 out4.0139 XPM225 B

ANfwhsyh…iYEHnbDU Ae8g7bM7…ZWghVkR9

0104ac6306e673…c74250a543dcf0

1 in → 2 out2.1602 XPM225 B

AcEGUXDj…JsRzHiLU AK3Bqb5F…py11CjtB

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.

1.763 × 10⁹⁶(97-digit number)

17637105785210258040…86348806018703103999

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

1.763 × 10⁹⁶(97-digit number)

17637105785210258040…86348806018703103999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.763 × 10⁹⁶(97-digit number)

17637105785210258040…86348806018703104001

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

3.527 × 10⁹⁶(97-digit number)

35274211570420516080…72697612037406207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.527 × 10⁹⁶(97-digit number)

35274211570420516080…72697612037406208001

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

7.054 × 10⁹⁶(97-digit number)

70548423140841032160…45395224074812415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.054 × 10⁹⁶(97-digit number)

70548423140841032160…45395224074812416001

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

1.410 × 10⁹⁷(98-digit number)

14109684628168206432…90790448149624831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.410 × 10⁹⁷(98-digit number)

14109684628168206432…90790448149624832001

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

2.821 × 10⁹⁷(98-digit number)

28219369256336412864…81580896299249663999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.821 × 10⁹⁷(98-digit number)

28219369256336412864…81580896299249664001

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