Block #2,653,611

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/8/2018, 1:26:01 PM · Difficulty 11.7352 · 4,180,123 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c80abf795de64bf93783b81998c415d8f140d97f820fdde62044f3d63bacbe8d

View on Chainz ↗

Height

#2,653,611

Difficulty

11.735191

Transactions

Size

425 B

Version

Bits

0bbc357e

Nonce

82,168,655

Timestamp

5/8/2018, 1:26:01 PM

Confirmations

4,180,123

Mined by

⛏️ P2SHAQrTdxxNH7zshz1xopLdugNUkv37CLqAqJ

Merkle Root

d65a600a22e76b0f567c20593cde62e3952bb77f61ed7917aa47af653580e9e3

Transactions (2)

Coinbasef10ea6e87b8a14…9568ae5aba2d7b

1 in → 1 out7.2600 XPM110 B

AQrTdxxN…37CLqAqJ

8cca571121718e…26b81b4e79dacd

1 in → 2 out1.1132 XPM226 B

AHmoHaoV…guxDRZ3w AYa4Ctbd…DQmhoxbV

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.

1.035 × 10⁹³(94-digit number)

10359687661024746696…20903495959158543349

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

1.035 × 10⁹³(94-digit number)

10359687661024746696…20903495959158543349

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.035 × 10⁹³(94-digit number)

10359687661024746696…20903495959158543351

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

2.071 × 10⁹³(94-digit number)

20719375322049493392…41806991918317086699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.071 × 10⁹³(94-digit number)

20719375322049493392…41806991918317086701

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

4.143 × 10⁹³(94-digit number)

41438750644098986784…83613983836634173399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.143 × 10⁹³(94-digit number)

41438750644098986784…83613983836634173401

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

8.287 × 10⁹³(94-digit number)

82877501288197973569…67227967673268346799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.287 × 10⁹³(94-digit number)

82877501288197973569…67227967673268346801

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

1.657 × 10⁹⁴(95-digit number)

16575500257639594713…34455935346536693599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.657 × 10⁹⁴(95-digit number)

16575500257639594713…34455935346536693601

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

3.315 × 10⁹⁴(95-digit number)

33151000515279189427…68911870693073387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

3.315 × 10⁹⁴(95-digit number)

33151000515279189427…68911870693073387201

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 #2,653,611

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