Block #301,423

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 4:41:19 AM · Difficulty 9.9925 · 6,506,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e38c753923a62a81b517153cf40c61b75a004dd7c7b274cf19f235533e33cc74

View on Chainz ↗

Height

#301,423

Difficulty

9.992523

Transactions

Size

1.17 KB

Version

Bits

09fe15fe

Nonce

590,629

Timestamp

12/9/2013, 4:41:19 AM

Confirmations

6,506,700

Mined by

⛏️ oaRI;>ASD5y7K3cnbxs1T4cNpuLUgeJZPadKp2tW

Merkle Root

b46ee447b0e31910bab526bf8c22406686caff78d18de4578aeea677a49bd910

Transactions (2)

Coinbasea5b572452c27df…c38f62fb00fb37

1 in → 24 out10.0000 XPM878 B

ASD5y7K3…PadKp2tW AcC2zSod…rtWatH79 AYcLTeXR…bscgPops AKwqFUdz…D4jGNKFN ASdFbQ41…WNAgRmiJ

b93b7d9424d1cc…3e9333cfd9e92b

1 in → 2 out1.1354 XPM225 B

AXtWJcJV…QdbSzzTC ANGHCphQ…Gubgy1HS

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.

1.353 × 10⁹⁶(97-digit number)

13532784044002252596…97938623153454463999

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

1.353 × 10⁹⁶(97-digit number)

13532784044002252596…97938623153454463999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.353 × 10⁹⁶(97-digit number)

13532784044002252596…97938623153454464001

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

2.706 × 10⁹⁶(97-digit number)

27065568088004505193…95877246306908927999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.706 × 10⁹⁶(97-digit number)

27065568088004505193…95877246306908928001

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

5.413 × 10⁹⁶(97-digit number)

54131136176009010386…91754492613817855999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.413 × 10⁹⁶(97-digit number)

54131136176009010386…91754492613817856001

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

1.082 × 10⁹⁷(98-digit number)

10826227235201802077…83508985227635711999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.082 × 10⁹⁷(98-digit number)

10826227235201802077…83508985227635712001

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

2.165 × 10⁹⁷(98-digit number)

21652454470403604154…67017970455271423999

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 #301,423

Cookie Preferences