Block #2,654,570

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/9/2018, 10:28:08 AM · Difficulty 11.7186 · 4,185,333 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b12c091817d4f8041278eb71557deb2a9201d5b440f2eb209d50139cdc13274

View on Chainz ↗

Height

#2,654,570

Difficulty

11.718649

Transactions

Size

870 B

Version

Bits

0bb7f95f

Nonce

355,769,927

Timestamp

5/9/2018, 10:28:08 AM

Confirmations

4,185,333

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

d0a0b501f0f7e7dd46be38042e1ae7ac1ba045ee634eb963a3c7d3309c60ebe4

Transactions (2)

Coinbase2da3576ac1fa25…cd5372c47fbfad

1 in → 1 out7.2800 XPM110 B

Adqah8zh…1WwoHJ9t

16264dd8d0322b…fb0ab5791afe65

4 in → 2 out1160.0106 XPM670 B

AWvhbTEe…XaNVbS8i AHx2ubCW…MpAapFgq

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.

4.328 × 10⁹³(94-digit number)

43282913937994415391…94460534506368750299

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

4.328 × 10⁹³(94-digit number)

43282913937994415391…94460534506368750299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.328 × 10⁹³(94-digit number)

43282913937994415391…94460534506368750301

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

8.656 × 10⁹³(94-digit number)

86565827875988830782…88921069012737500599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.656 × 10⁹³(94-digit number)

86565827875988830782…88921069012737500601

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

1.731 × 10⁹⁴(95-digit number)

17313165575197766156…77842138025475001199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.731 × 10⁹⁴(95-digit number)

17313165575197766156…77842138025475001201

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

3.462 × 10⁹⁴(95-digit number)

34626331150395532312…55684276050950002399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.462 × 10⁹⁴(95-digit number)

34626331150395532312…55684276050950002401

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

6.925 × 10⁹⁴(95-digit number)

69252662300791064625…11368552101900004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.925 × 10⁹⁴(95-digit number)

69252662300791064625…11368552101900004801

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

1.385 × 10⁹⁵(96-digit number)

13850532460158212925…22737104203800009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.385 × 10⁹⁵(96-digit number)

13850532460158212925…22737104203800009601

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 #2,654,570

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