Block #247,561

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 8:23:03 PM · Difficulty 9.9650 · 6,566,653 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f38a5c651feffbbfa11b6dca2c412c009fa0eee4314915650add10fe511ff143

View on Chainz ↗

Height

#247,561

Difficulty

9.965025

Transactions

Size

2.08 KB

Version

Bits

09f70bdb

Nonce

10,877

Timestamp

11/6/2013, 8:23:03 PM

Confirmations

6,566,653

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

b5c62be5d636af615c9dfe749b4fac5453d4b3dbc385eafd1bee27c2720203b2

Transactions (4)

Coinbase1205912fff4fe8…2f7c619e7b720e

1 in → 2 out10.0900 XPM142 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

ef32c443e17fb3…5bb9f8103bdc23

4 in → 5 out14.9399 XPM740 B

AbY55x6i…T8gf2Zvm AVKfZvtY…sCa4NTcM AL7194fk…YNQBVjTB AeKNrjNj…1NEq95Ta AdzxCrFi…bGGMrU9D

67960c76a11dc0…335abcb09f12b2

6 in → 2 out6.6167 XPM966 B

AR2G3pyK…mUUptrde AU8wXwsR…Unb6ZWxS

48735630b41c8c…5e0340a3cdb3ee

1 in → 1 out134.2103 XPM192 B

ATknEwpv…tz6xvy1e

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.

1.075 × 10⁹⁶(97-digit number)

10759836333689213742…93130853655543751849

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

1.075 × 10⁹⁶(97-digit number)

10759836333689213742…93130853655543751849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.075 × 10⁹⁶(97-digit number)

10759836333689213742…93130853655543751851

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

2.151 × 10⁹⁶(97-digit number)

21519672667378427484…86261707311087503699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.151 × 10⁹⁶(97-digit number)

21519672667378427484…86261707311087503701

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

4.303 × 10⁹⁶(97-digit number)

43039345334756854969…72523414622175007399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.303 × 10⁹⁶(97-digit number)

43039345334756854969…72523414622175007401

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

8.607 × 10⁹⁶(97-digit number)

86078690669513709939…45046829244350014799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.607 × 10⁹⁶(97-digit number)

86078690669513709939…45046829244350014801

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

1.721 × 10⁹⁷(98-digit number)

17215738133902741987…90093658488700029599

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 #247,561

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