Block #248,091

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 4:14:57 AM · Difficulty 9.9654 · 6,567,053 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95b71a655c4ae7327b6ab7113157e860e55d909af937af1c41f1b99b91d060d8

View on Chainz ↗

Height

#248,091

Difficulty

9.965442

Transactions

Size

1.97 KB

Version

Bits

09f72733

Nonce

3,681

Timestamp

11/7/2013, 4:14:57 AM

Confirmations

6,567,053

Mined by

⛏️ R{AMMzjz3cBgHw72qLAVsoX9nqknMjrvoC8k

Merkle Root

e7b8183d203607ee0c51ae96850a873e58eb4cf30f60d320067f37a829c980b9

Transactions (1)

Coinbasee7b8183d203607…7f37a829c980b9

1 in → 55 out10.0300 XPM1.89 KB

AMMzjz3c…MjrvoC8k ANpPrsJp…YzdEphWb AdL4ZZDR…2eQtg1T9 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

2.660 × 10⁹³(94-digit number)

26607352027058651717…65066166223317140799

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

2.660 × 10⁹³(94-digit number)

26607352027058651717…65066166223317140799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.660 × 10⁹³(94-digit number)

26607352027058651717…65066166223317140801

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

5.321 × 10⁹³(94-digit number)

53214704054117303434…30132332446634281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.321 × 10⁹³(94-digit number)

53214704054117303434…30132332446634281601

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

1.064 × 10⁹⁴(95-digit number)

10642940810823460686…60264664893268563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.064 × 10⁹⁴(95-digit number)

10642940810823460686…60264664893268563201

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

2.128 × 10⁹⁴(95-digit number)

21285881621646921373…20529329786537126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.128 × 10⁹⁴(95-digit number)

21285881621646921373…20529329786537126401

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

4.257 × 10⁹⁴(95-digit number)

42571763243293842747…41058659573074252799

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 #248,091

Cookie Preferences