Block #3,153,520

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/24/2019, 2:29:30 PM · Difficulty 11.3209 · 3,688,509 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

90c1626d5103c89e7864d1719fb318cd62aef32c1cb94c82c083d093729a29d1

View on Chainz ↗

Height

#3,153,520

Difficulty

11.320862

Transactions

Size

541 B

Version

Bits

0b522402

Nonce

1,729,346,961

Timestamp

4/24/2019, 2:29:30 PM

Confirmations

3,688,509

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

8f9c4b9801d3ecc2529ea67a5620a31f09acb8e401c8607ae25914f1fdcfce21

Transactions (2)

Coinbase5209ae3e28ccdf…cca4ca5baabf4b

1 in → 1 out7.8000 XPM110 B

AbXwmGxD…4XXYP765

4c56d2dfea4d43…d91610e86d3165

2 in → 2 out13.3700 XPM340 B

AQ8W1pW5…uqCFR9Pf APVKWthF…PMMxwRoz

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.

1.143 × 10⁹⁷(98-digit number)

11435307733643899676…89327896646534525439

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

1.143 × 10⁹⁷(98-digit number)

11435307733643899676…89327896646534525439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.143 × 10⁹⁷(98-digit number)

11435307733643899676…89327896646534525441

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

2.287 × 10⁹⁷(98-digit number)

22870615467287799352…78655793293069050879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.287 × 10⁹⁷(98-digit number)

22870615467287799352…78655793293069050881

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

4.574 × 10⁹⁷(98-digit number)

45741230934575598705…57311586586138101759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.574 × 10⁹⁷(98-digit number)

45741230934575598705…57311586586138101761

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

9.148 × 10⁹⁷(98-digit number)

91482461869151197410…14623173172276203519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.148 × 10⁹⁷(98-digit number)

91482461869151197410…14623173172276203521

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

1.829 × 10⁹⁸(99-digit number)

18296492373830239482…29246346344552407039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.829 × 10⁹⁸(99-digit number)

18296492373830239482…29246346344552407041

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

3.659 × 10⁹⁸(99-digit number)

36592984747660478964…58492692689104814079

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 #3,153,520

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