Block #2,653,055

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2018, 2:21:28 AM · Difficulty 11.7406 · 4,178,184 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2ba5dc0e15853c0fc2153b0affa24e7996f98cb7bfb3412b0d6d8e888863307

View on Chainz ↗

Height

#2,653,055

Difficulty

11.740649

Transactions

Size

576 B

Version

Bits

0bbd9b2e

Nonce

2,102,782,219

Timestamp

5/8/2018, 2:21:28 AM

Confirmations

4,178,184

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

258fac3344e03bcae8d71a6e74068c2974cd54c1f9757bace815566cc5613364

Transactions (2)

Coinbasea5dad4e10b5528…91bd0c652cf5b2

1 in → 1 out7.2500 XPM110 B

Adqah8zh…1WwoHJ9t

4583cc1a86052f…491001534888a5

2 in → 2 out4.3515 XPM374 B

ALFCjDjB…XEfXtzaq AbzVivCR…AGJbSBdK

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.

5.625 × 10⁹⁹(100-digit number)

56253177152390710553…41756808804522393599

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

5.625 × 10⁹⁹(100-digit number)

56253177152390710553…41756808804522393599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.625 × 10⁹⁹(100-digit number)

56253177152390710553…41756808804522393601

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

1.125 × 10¹⁰⁰(101-digit number)

11250635430478142110…83513617609044787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.125 × 10¹⁰⁰(101-digit number)

11250635430478142110…83513617609044787201

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

2.250 × 10¹⁰⁰(101-digit number)

22501270860956284221…67027235218089574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.250 × 10¹⁰⁰(101-digit number)

22501270860956284221…67027235218089574401

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

4.500 × 10¹⁰⁰(101-digit number)

45002541721912568443…34054470436179148799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.500 × 10¹⁰⁰(101-digit number)

45002541721912568443…34054470436179148801

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

9.000 × 10¹⁰⁰(101-digit number)

90005083443825136886…68108940872358297599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.000 × 10¹⁰⁰(101-digit number)

90005083443825136886…68108940872358297601

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

1.800 × 10¹⁰¹(102-digit number)

18001016688765027377…36217881744716595199

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 #2,653,055

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