Block #249,975

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 6:35:29 AM · Difficulty 9.9675 · 6,555,222 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40766a2868c84a2b0b21c0e59de37352e158cf7ec3f18a90100e0a84b6b44650

View on Chainz ↗

Height

#249,975

Difficulty

9.967542

Transactions

Size

1.03 KB

Version

Bits

09f7b0dd

Nonce

9,128

Timestamp

11/8/2013, 6:35:29 AM

Confirmations

6,555,222

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

bc49e6eda183da6f6342c0949017c4fa240407a12eecb36780c639c62438d3d3

Transactions (4)

Coinbasea9b36f59888cb7…45532be82df9a0

1 in → 2 out10.0825 XPM142 B

AdGRRh1e…QmctLb24 AHsw4d6U…EnM8UXNZ

c097d2175d84fd…154a8c73a045b5

1 in → 2 out10.0500 XPM226 B

AcM4842Z…eGXdTJ6H ASuoUi24…FwBoFbxd

1172d05d3f0b48…e1655a946ebdf2

1 in → 4 out10.0500 XPM260 B

AeKNrjNj…1NEq95Ta AWP3nWpc…wKY1EyHx AcyPVp7N…dDULWcdA AdzxCrFi…bGGMrU9D

b43cd15eeebcd0…7932929cf461ab

2 in → 1 out6.2900 XPM339 B

AJyFniav…ysbLRLjJ

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.

4.968 × 10⁹⁶(97-digit number)

49686607273455973379…00409844874983834559

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

4.968 × 10⁹⁶(97-digit number)

49686607273455973379…00409844874983834559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.968 × 10⁹⁶(97-digit number)

49686607273455973379…00409844874983834561

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

9.937 × 10⁹⁶(97-digit number)

99373214546911946759…00819689749967669119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.937 × 10⁹⁶(97-digit number)

99373214546911946759…00819689749967669121

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

1.987 × 10⁹⁷(98-digit number)

19874642909382389351…01639379499935338239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.987 × 10⁹⁷(98-digit number)

19874642909382389351…01639379499935338241

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

3.974 × 10⁹⁷(98-digit number)

39749285818764778703…03278758999870676479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.974 × 10⁹⁷(98-digit number)

39749285818764778703…03278758999870676481

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

7.949 × 10⁹⁷(98-digit number)

79498571637529557407…06557517999741352959

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