Block #267,110

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 11:56:41 PM · Difficulty 9.9597 · 6,524,661 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fed24afe93cf9184c7c12d321eebc440da41fbb2955ed250f73f9445af7150fa

View on Chainz ↗

Height

#267,110

Difficulty

9.959740

Transactions

Size

428 B

Version

Bits

09f5b17f

Nonce

18,813

Timestamp

11/20/2013, 11:56:41 PM

Confirmations

6,524,661

Merkle Root

74c80616370bd10a4c875b33238fb56214a1403b9aa64530b2a775e884985a50

Transactions (2)

Coinbase24e8dcaf29056a…6cf9e14c2f88be

1 in → 1 out10.0800 XPM109 B

AZfuXsHD…RhN4QwMr

81462d122b18e5…043ddb6db86660

1 in → 2 out3.9395 XPM226 B

AeKNrjNj…1NEq95Ta AMuPGPXT…eMMNvd8v

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.

4.229 × 10¹⁰²(103-digit number)

42299026775790661393…92954945106908227839

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

4.229 × 10¹⁰²(103-digit number)

42299026775790661393…92954945106908227839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.229 × 10¹⁰²(103-digit number)

42299026775790661393…92954945106908227841

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

8.459 × 10¹⁰²(103-digit number)

84598053551581322787…85909890213816455679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.459 × 10¹⁰²(103-digit number)

84598053551581322787…85909890213816455681

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

1.691 × 10¹⁰³(104-digit number)

16919610710316264557…71819780427632911359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.691 × 10¹⁰³(104-digit number)

16919610710316264557…71819780427632911361

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

3.383 × 10¹⁰³(104-digit number)

33839221420632529115…43639560855265822719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.383 × 10¹⁰³(104-digit number)

33839221420632529115…43639560855265822721

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

6.767 × 10¹⁰³(104-digit number)

67678442841265058230…87279121710531645439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.767 × 10¹⁰³(104-digit number)

67678442841265058230…87279121710531645441

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