Block #246,634

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 6:46:42 AM · Difficulty 9.9642 · 6,577,964 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

392edf19701f17e72459a65363b3316611b483a58827ff8f19c5aefa472bd646

View on Chainz ↗

Height

#246,634

Difficulty

9.964206

Transactions

Size

1.76 KB

Version

Bits

09f6d62d

Nonce

27,575

Timestamp

11/6/2013, 6:46:42 AM

Confirmations

6,577,964

Mined by

⛏️ jRyAdmbm7GQnn33eHw9DjTNwmi7vV6FpYbg8G

Merkle Root

9f5e711b6358ae30bb10dd5fbf3a2cc3836a5f91c290f1221fc69837374a9ac1

Transactions (2)

Coinbase1f3c95a3518779…eee3343ea9b401

1 in → 42 out10.0400 XPM1.46 KB

Admbm7GQ…6FpYbg8G ARpndEmc…Hg792kEk ANUaggy4…MWdrertQ AcEnwywz…vZtt2xTs AJzWx2VD…j4ZSMit5

eb1709fecde0b0…9f58513683c3dd

1 in → 2 out10.0500 XPM226 B

ARmHDN8B…h3wsnrst AXER7WQd…sgk8Muj3

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.

1.319 × 10⁹⁶(97-digit number)

13197696233266100690…78860406226005817599

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

1.319 × 10⁹⁶(97-digit number)

13197696233266100690…78860406226005817599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.319 × 10⁹⁶(97-digit number)

13197696233266100690…78860406226005817601

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

2.639 × 10⁹⁶(97-digit number)

26395392466532201381…57720812452011635199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.639 × 10⁹⁶(97-digit number)

26395392466532201381…57720812452011635201

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

5.279 × 10⁹⁶(97-digit number)

52790784933064402763…15441624904023270399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.279 × 10⁹⁶(97-digit number)

52790784933064402763…15441624904023270401

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

1.055 × 10⁹⁷(98-digit number)

10558156986612880552…30883249808046540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.055 × 10⁹⁷(98-digit number)

10558156986612880552…30883249808046540801

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

2.111 × 10⁹⁷(98-digit number)

21116313973225761105…61766499616093081599

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 #246,634

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