Block #238,119

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 9:48:33 AM · Difficulty 9.9514 · 6,551,715 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

47c9d820de7d3e552903ff7928d40dd713ac50d7bbdf655bc1527dd2fd6d4b38

View on Chainz ↗

Height

#238,119

Difficulty

9.951391

Transactions

Size

3.60 KB

Version

Bits

09f38e5d

Nonce

35,662

Timestamp

11/1/2013, 9:48:33 AM

Confirmations

6,551,715

Merkle Root

9bad12ca88cdc20379779c442e0836ae468217067228d5672a19f13ca83f2ea7

Transactions (5)

Coinbase2558d9a27e1061…c1aab9960b2583

1 in → 1 out10.1496 XPM109 B

AUU7jbYC…MpCVGPie

1ef9512acce4ee…3553c48a91b735

18 in → 1 out164.4400 XPM2.12 KB

AaZTHvEh…QXHS2iBB

4bf47d9500ac51…c18270e28909fd

4 in → 2 out31.4200 XPM568 B

AWKpUf5f…S2RLN5dS AZv7gMUK…CbiASjGW

0d891245986984…22bfbbac9cad9d

3 in → 2 out28.2630 XPM523 B

AMENkQkx…6pYQqASQ Abxn3EEB…8ccf7zVj

0ebcd539418ce2…c68f09720cedcc

1 in → 2 out5.8471 XPM227 B

AGf8YTJX…mPnX5s2c AGyXwxsG…fteuYo4f

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.

3.528 × 10⁹⁶(97-digit number)

35280093920818897019…82300944295754820799

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

3.528 × 10⁹⁶(97-digit number)

35280093920818897019…82300944295754820799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.528 × 10⁹⁶(97-digit number)

35280093920818897019…82300944295754820801

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

7.056 × 10⁹⁶(97-digit number)

70560187841637794038…64601888591509641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.056 × 10⁹⁶(97-digit number)

70560187841637794038…64601888591509641601

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

1.411 × 10⁹⁷(98-digit number)

14112037568327558807…29203777183019283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.411 × 10⁹⁷(98-digit number)

14112037568327558807…29203777183019283201

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

2.822 × 10⁹⁷(98-digit number)

28224075136655117615…58407554366038566399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.822 × 10⁹⁷(98-digit number)

28224075136655117615…58407554366038566401

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

5.644 × 10⁹⁷(98-digit number)

56448150273310235231…16815108732077132799

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