Block #267,020

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 9:56:16 PM · Difficulty 9.9600 · 6,523,985 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b06ff8d796304315ca3c52f79fa6c30913e5f16f77817d0906a62dd0cce39493

View on Chainz ↗

Height

#267,020

Difficulty

9.959978

Transactions

Size

461 B

Version

Bits

09f5c116

Nonce

25,653

Timestamp

11/20/2013, 9:56:16 PM

Confirmations

6,523,985

Merkle Root

b4738bab95a9be1ff2574a87ea9f1f8f7e560c2d8ded8a360e3474f6513b4abc

Transactions (2)

Coinbase2ffdcc663a090f…5267e701db42f6

1 in → 2 out10.0800 XPM142 B

AdGRRh1e…QmctLb24 ASNt3cJa…L5zCqAYM

360cc3adc44fd5…b8b16f37d60571

1 in → 3 out10.0500 XPM226 B

AeKNrjNj…1NEq95Ta AYiuPkxV…9nUvdUg1 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.

1.045 × 10¹⁰³(104-digit number)

10450566394727220727…27270892059973301759

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

1.045 × 10¹⁰³(104-digit number)

10450566394727220727…27270892059973301759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.045 × 10¹⁰³(104-digit number)

10450566394727220727…27270892059973301761

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

2.090 × 10¹⁰³(104-digit number)

20901132789454441454…54541784119946603519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.090 × 10¹⁰³(104-digit number)

20901132789454441454…54541784119946603521

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

4.180 × 10¹⁰³(104-digit number)

41802265578908882908…09083568239893207039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.180 × 10¹⁰³(104-digit number)

41802265578908882908…09083568239893207041

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

8.360 × 10¹⁰³(104-digit number)

83604531157817765816…18167136479786414079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.360 × 10¹⁰³(104-digit number)

83604531157817765816…18167136479786414081

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

1.672 × 10¹⁰⁴(105-digit number)

16720906231563553163…36334272959572828159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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