Block #272,275

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 4:09:19 AM · Difficulty 9.9526 · 6,531,381 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e6cd9045f6e09085dc4f0b07ebb2758417c692b0d575c77580c38f7d02e9405

View on Chainz ↗

Height

#272,275

Difficulty

9.952583

Transactions

Size

5.84 KB

Version

Bits

09f3dc7f

Nonce

12,398

Timestamp

11/25/2013, 4:09:19 AM

Confirmations

6,531,381

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

9668c6817173ecf32909367f86db836dcf0863665a7a43193c2d1d82e0dd3495

Transactions (5)

Coinbase60b2030bb6eb31…be837a41fb7f2a

1 in → 2 out10.1700 XPM141 B

AdGRRh1e…QmctLb24 AKNbfPoc…jfkpwAyL

0c6de0900ca06a…44dd2f2ddac1c0

3 in → 2 out2206.6700 XPM521 B

AdU6KrrW…RfCHehM4 AayaEzGc…tq6zxky9

1c1e9716f45c47…69d83e7ae83a26

18 in → 1 out201.9900 XPM2.64 KB

AL6YsAFg…r4BgGWgi

d6735d023d0de0…8092873a2c8c02

1 in → 2 out9.9900 XPM227 B

AY4H42CP…4bQ4ZA3H AbH661jc…2oZyzbc7

2fb2854fa56b8c…ae258786a8c379

15 in → 2 out1.7285 XPM2.24 KB

AbKiRuZR…JLeBpT8j AbyCzpQh…2ATXt5v6

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.

6.295 × 10¹⁰⁴(105-digit number)

62953271766049089464…29142212304683095039

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

6.295 × 10¹⁰⁴(105-digit number)

62953271766049089464…29142212304683095039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.295 × 10¹⁰⁴(105-digit number)

62953271766049089464…29142212304683095041

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

1.259 × 10¹⁰⁵(106-digit number)

12590654353209817892…58284424609366190079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.259 × 10¹⁰⁵(106-digit number)

12590654353209817892…58284424609366190081

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

2.518 × 10¹⁰⁵(106-digit number)

25181308706419635785…16568849218732380159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.518 × 10¹⁰⁵(106-digit number)

25181308706419635785…16568849218732380161

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

5.036 × 10¹⁰⁵(106-digit number)

50362617412839271571…33137698437464760319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.036 × 10¹⁰⁵(106-digit number)

50362617412839271571…33137698437464760321

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

1.007 × 10¹⁰⁶(107-digit number)

10072523482567854314…66275396874929520639

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