Block #3,294,234

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 8/3/2019, 5:49:26 PM · Difficulty 10.9951 · 3,530,264 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b3838f0863a1a960fc2459ec6ea2c265c78a8a8b5572708db407f2d1ccb092d

View on Chainz ↗

Height

#3,294,234

Difficulty

10.995147

Transactions

Size

3.71 KB

Version

Bits

0afec1fa

Nonce

545,459,409

Timestamp

8/3/2019, 5:49:26 PM

Confirmations

3,530,264

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

248d1102df7eeb9b2019b8f35fde44968cb2bde1169eb741feca890c3dd71901

Transactions (4)

Coinbase7439dd93a77366…529524d615d236

1 in → 1 out8.3200 XPM110 B

ASiq2qtK…VMhmk7yL

7dda2d985af834…3634143ea374e4

14 in → 2 out101.2404 XPM1.70 KB

AemY4Zt4…87UF1iHf ASiq2qtK…VMhmk7yL

386f673c81697b…9c11cc14394a11

13 in → 2 out94.0740 XPM1.59 KB

ATXgwL2J…MFRhJQUP ASiq2qtK…VMhmk7yL

cba4b3a0ef6be3…b34d4afbb58553

1 in → 2 out0.1495 XPM226 B

ASiq2qtK…VMhmk7yL AcRnr7wg…DHyLGdxh

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.

1.521 × 10⁹⁴(95-digit number)

15210741261881796171…18114646607054756999

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

1.521 × 10⁹⁴(95-digit number)

15210741261881796171…18114646607054756999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.521 × 10⁹⁴(95-digit number)

15210741261881796171…18114646607054757001

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

3.042 × 10⁹⁴(95-digit number)

30421482523763592342…36229293214109513999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.042 × 10⁹⁴(95-digit number)

30421482523763592342…36229293214109514001

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

6.084 × 10⁹⁴(95-digit number)

60842965047527184684…72458586428219027999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.084 × 10⁹⁴(95-digit number)

60842965047527184684…72458586428219028001

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

1.216 × 10⁹⁵(96-digit number)

12168593009505436936…44917172856438055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.216 × 10⁹⁵(96-digit number)

12168593009505436936…44917172856438056001

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

2.433 × 10⁹⁵(96-digit number)

24337186019010873873…89834345712876111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.433 × 10⁹⁵(96-digit number)

24337186019010873873…89834345712876112001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.867 × 10⁹⁵(96-digit number)

48674372038021747747…79668691425752223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

4.867 × 10⁹⁵(96-digit number)

48674372038021747747…79668691425752224001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #3,294,234

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