Block #3,123,488

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/3/2019, 5:51:27 PM · Difficulty 11.3201 · 3,716,187 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

269c37f43104013a1ee436961e4cd47a8547082e1dde0c8fde4a3d21f4cf04cd

View on Chainz ↗

Height

#3,123,488

Difficulty

11.320135

Transactions

Size

2.73 KB

Version

Bits

0b51f456

Nonce

578,516,993

Timestamp

4/3/2019, 5:51:27 PM

Confirmations

3,716,187

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

e42cfcb6181a6e908daf2e8c79d218141b3c4aa8b4da1a2997800ee58e88421b

Transactions (2)

Coinbased622ffca734b10…a2449e58b366b4

1 in → 1 out8.0300 XPM110 B

AbXwmGxD…4XXYP765

b5c93a54b16a8c…e32c4850152bc2

17 in → 2 out29941.1305 XPM2.53 KB

AQdABV2g…6jsa34vM ARQBQiFS…uxviAzfZ

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.

1.631 × 10⁹⁶(97-digit number)

16318260802084608857…92615370439752307199

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

1.631 × 10⁹⁶(97-digit number)

16318260802084608857…92615370439752307199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.631 × 10⁹⁶(97-digit number)

16318260802084608857…92615370439752307201

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

3.263 × 10⁹⁶(97-digit number)

32636521604169217714…85230740879504614399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.263 × 10⁹⁶(97-digit number)

32636521604169217714…85230740879504614401

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

6.527 × 10⁹⁶(97-digit number)

65273043208338435429…70461481759009228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.527 × 10⁹⁶(97-digit number)

65273043208338435429…70461481759009228801

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

1.305 × 10⁹⁷(98-digit number)

13054608641667687085…40922963518018457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.305 × 10⁹⁷(98-digit number)

13054608641667687085…40922963518018457601

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

2.610 × 10⁹⁷(98-digit number)

26109217283335374171…81845927036036915199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.610 × 10⁹⁷(98-digit number)

26109217283335374171…81845927036036915201

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

5.221 × 10⁹⁷(98-digit number)

52218434566670748343…63691854072073830399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #3,123,488

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