Block #298,247

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 5:13:34 AM · Difficulty 9.9919 · 6,544,638 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d431c34fc6e982fb1b311f678b1ea12771f5383ca5099837936c315fb5974f89

View on Chainz ↗

Height

#298,247

Difficulty

9.991910

Transactions

Size

1.01 KB

Version

Bits

09fdedc9

Nonce

3,454

Timestamp

12/7/2013, 5:13:34 AM

Confirmations

6,544,638

Mined by

⛏️ aRAPfZjrNuhmjAdWEndZTiR9g2XrWvzt6AFp

Merkle Root

aa3b4d69c57cfcfbac7b1d15ed5ad6b9bd9827340b7cf681c66221a66df75c8a

Transactions (1)

Coinbaseaa3b4d69c57cfc…6221a66df75c8a

1 in → 26 out10.0000 XPM947 B

APfZjrNu…Wvzt6AFp ASPzomex…JkjSwA1z AWhrzPUm…CvuNWn8t AKEwr54i…9BfmMkRh AHjeGKcH…bHTM7J43

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.

1.451 × 10⁹³(94-digit number)

14518322297286056980…87801550258608191999

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

1.451 × 10⁹³(94-digit number)

14518322297286056980…87801550258608191999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.451 × 10⁹³(94-digit number)

14518322297286056980…87801550258608192001

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

2.903 × 10⁹³(94-digit number)

29036644594572113960…75603100517216383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.903 × 10⁹³(94-digit number)

29036644594572113960…75603100517216384001

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

5.807 × 10⁹³(94-digit number)

58073289189144227921…51206201034432767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.807 × 10⁹³(94-digit number)

58073289189144227921…51206201034432768001

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

1.161 × 10⁹⁴(95-digit number)

11614657837828845584…02412402068865535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.161 × 10⁹⁴(95-digit number)

11614657837828845584…02412402068865536001

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

2.322 × 10⁹⁴(95-digit number)

23229315675657691168…04824804137731071999

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

Block #298,247

Cookie Preferences