Block #238,417

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 1:25:50 PM · Difficulty 9.9522 · 6,571,788 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e404d5e0788fea6a80cdb5ff6a68c7669f33dada9e7f5aca4bbde1bcd67b8168

View on Chainz ↗

Height

#238,417

Difficulty

9.952176

Transactions

Size

1.98 KB

Version

Bits

09f3c1d2

Nonce

38,410

Timestamp

11/1/2013, 1:25:50 PM

Confirmations

6,571,788

Mined by

⛏️ QRsJAKwqFUdzFNyMbekqhPUpd29CZJD4jGNKFN

Merkle Root

66ef3f63d6378e706a8502795db3ba2d906c44ddbde6ec8d7d905c970d1f64eb

Transactions (1)

Coinbase66ef3f63d6378e…905c970d1f64eb

1 in → 55 out10.0600 XPM1.89 KB

AKwqFUdz…D4jGNKFN ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AG9H2B8p…eiaSPdGS

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.

1.045 × 10⁹⁷(98-digit number)

10450262048600781577…99170928083872172799

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

1.045 × 10⁹⁷(98-digit number)

10450262048600781577…99170928083872172799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.045 × 10⁹⁷(98-digit number)

10450262048600781577…99170928083872172801

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

2.090 × 10⁹⁷(98-digit number)

20900524097201563155…98341856167744345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.090 × 10⁹⁷(98-digit number)

20900524097201563155…98341856167744345601

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

4.180 × 10⁹⁷(98-digit number)

41801048194403126311…96683712335488691199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.180 × 10⁹⁷(98-digit number)

41801048194403126311…96683712335488691201

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

8.360 × 10⁹⁷(98-digit number)

83602096388806252623…93367424670977382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.360 × 10⁹⁷(98-digit number)

83602096388806252623…93367424670977382401

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

1.672 × 10⁹⁸(99-digit number)

16720419277761250524…86734849341954764799

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 #238,417

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