Block #2,913,128

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/7/2018, 2:30:55 AM · Difficulty 11.4988 · 3,926,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d4601dbf7df19d03bcb3963ce07bf24f54f5a7d1582213b51074d27df6ae7d7d

View on Chainz ↗

Height

#2,913,128

Difficulty

11.498828

Transactions

Size

1.51 KB

Version

Bits

0b7fb334

Nonce

1,555,242,456

Timestamp

11/7/2018, 2:30:55 AM

Confirmations

3,926,365

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

61e81e8426891f0b0314ff76bc878ee625090d7c60a5b22c5abcb2f35bc5ba5d

Transactions (5)

Coinbase0a2f0963b4f8e9…97b488859d2072

1 in → 1 out7.5900 XPM110 B

AUMQRepm…tAfKmdW1

9f56b5a8011034…0ed56175edd827

1 in → 2 out6.5100 XPM225 B

AMwwthF9…ooKey3B9 ALjnEVst…U3zEc4hk

a29a540a84855c…72ca186668472c

2 in → 2 out6.9700 XPM376 B

AGvNyEui…uUbMr2AS AM5LHK74…koZFkVon

0a39231a9b3a0b…471687edfffc84

2 in → 2 out6.4500 XPM372 B

AaJHr1p3…vJhJ8J2T AJvKjLrt…dfxfFtt3

144a2ad7afce13…0f83a2b443a9dc

2 in → 2 out5.9400 XPM373 B

ASiZbdG9…zFWWmpBp AJaWK7oJ…sNMWsTji

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.

1.543 × 10⁹⁴(95-digit number)

15438397312386368289…14778958857597861599

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

1.543 × 10⁹⁴(95-digit number)

15438397312386368289…14778958857597861599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.543 × 10⁹⁴(95-digit number)

15438397312386368289…14778958857597861601

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

3.087 × 10⁹⁴(95-digit number)

30876794624772736578…29557917715195723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.087 × 10⁹⁴(95-digit number)

30876794624772736578…29557917715195723201

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

6.175 × 10⁹⁴(95-digit number)

61753589249545473156…59115835430391446399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.175 × 10⁹⁴(95-digit number)

61753589249545473156…59115835430391446401

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

1.235 × 10⁹⁵(96-digit number)

12350717849909094631…18231670860782892799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.235 × 10⁹⁵(96-digit number)

12350717849909094631…18231670860782892801

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

2.470 × 10⁹⁵(96-digit number)

24701435699818189262…36463341721565785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.470 × 10⁹⁵(96-digit number)

24701435699818189262…36463341721565785601

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

4.940 × 10⁹⁵(96-digit number)

49402871399636378525…72926683443131571199

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 #2,913,128

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