Block #273,207

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 4:33:28 PM · Difficulty 9.9543 · 6,518,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c737f802a5338db454226e04c50cba743620cf70316d3c004f219e330d0b818

View on Chainz ↗

Height

#273,207

Difficulty

9.954340

Transactions

Size

3.09 KB

Version

Bits

09f44f99

Nonce

1,356

Timestamp

11/25/2013, 4:33:28 PM

Confirmations

6,518,211

Merkle Root

2d9e5c01c57acb02f38818e5ecdebc6bd983285c6e6470b57a2b3cc843b98f2e

Transactions (3)

Coinbaseb4f31454fd1683…e141ec41988d5e

1 in → 1 out10.1300 XPM109 B

AYbFBdKz…cf926Mct

153f6232332c03…5331594cbd8e2a

18 in → 2 out216.4410 XPM2.68 KB

AW23Tdpc…GJuVRajT AGtbsxqx…fEjmbE2i

07d4640ce4d379…9dd8154514f106

1 in → 2 out8.0484 XPM225 B

AHL2VVqd…zDNYuQiZ AaVFHFSq…bCnX1Bpw

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.

9.452 × 10⁹⁴(95-digit number)

94525602510276329694…48799295811708912639

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

9.452 × 10⁹⁴(95-digit number)

94525602510276329694…48799295811708912639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.452 × 10⁹⁴(95-digit number)

94525602510276329694…48799295811708912641

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

1.890 × 10⁹⁵(96-digit number)

18905120502055265938…97598591623417825279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.890 × 10⁹⁵(96-digit number)

18905120502055265938…97598591623417825281

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

3.781 × 10⁹⁵(96-digit number)

37810241004110531877…95197183246835650559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.781 × 10⁹⁵(96-digit number)

37810241004110531877…95197183246835650561

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

7.562 × 10⁹⁵(96-digit number)

75620482008221063755…90394366493671301119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.562 × 10⁹⁵(96-digit number)

75620482008221063755…90394366493671301121

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

1.512 × 10⁹⁶(97-digit number)

15124096401644212751…80788732987342602239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.512 × 10⁹⁶(97-digit number)

15124096401644212751…80788732987342602241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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