Block #1,124,909

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/24/2015, 9:40:08 AM · Difficulty 10.9337 · 5,682,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4866bc22bd99346fdc9493163fd5200fac453d6898502ae4a77741842cf1d209

View on Chainz ↗

Height

#1,124,909

Difficulty

10.933669

Transactions

Size

730 B

Version

Bits

0aef04e8

Nonce

2,207,964,550

Timestamp

6/24/2015, 9:40:08 AM

Confirmations

5,682,214

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

46c8bdb4b101aafe7a873cf921edff9466b10a891ca8da6ff8103595cd7baa8b

Transactions (2)

Coinbase82449e3729371d…c7b90868c86948

1 in → 1 out8.3600 XPM116 B

AJCEY9yy…tg97E6zm

d652dd1fe974ec…f4989df3530bf8

3 in → 2 out3.7777 XPM523 B

AVYjNJEW…jTeas9v4 AbCQ5rxt…JDcTKXr5

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.

3.458 × 10⁹⁷(98-digit number)

34583140376087646881…23595864763154677759

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

3.458 × 10⁹⁷(98-digit number)

34583140376087646881…23595864763154677759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.458 × 10⁹⁷(98-digit number)

34583140376087646881…23595864763154677761

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

6.916 × 10⁹⁷(98-digit number)

69166280752175293762…47191729526309355519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.916 × 10⁹⁷(98-digit number)

69166280752175293762…47191729526309355521

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

1.383 × 10⁹⁸(99-digit number)

13833256150435058752…94383459052618711039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.383 × 10⁹⁸(99-digit number)

13833256150435058752…94383459052618711041

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

2.766 × 10⁹⁸(99-digit number)

27666512300870117504…88766918105237422079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.766 × 10⁹⁸(99-digit number)

27666512300870117504…88766918105237422081

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

5.533 × 10⁹⁸(99-digit number)

55333024601740235009…77533836210474844159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.533 × 10⁹⁸(99-digit number)

55333024601740235009…77533836210474844161

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 #1,124,909

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