Block #2,823,970

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/4/2018, 6:29:00 AM · Difficulty 11.7077 · 4,019,763 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa26c28322283112a26affa4908e2ea5965145dba819b350b77e728ac246bdf8

View on Chainz ↗

Height

#2,823,970

Difficulty

11.707700

Transactions

Size

732 B

Version

Bits

0bb52bcd

Nonce

247,518,829

Timestamp

9/4/2018, 6:29:00 AM

Confirmations

4,019,763

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

aa455e72b315fcff591d9598ba631b25802914a054d59bd72e49cbd34a73896c

Transactions (2)

Coinbase205a978c00fb77…b5fdf2d434fc1e

1 in → 1 out7.2900 XPM110 B

AZtxQr2F…7grUWrUz

85e3c6644b49ec…d3986b38226201

1 in → 11 out15.0149 XPM532 B

AJxaziwh…wLkxs8ji APfWKUxH…1CQZXRoy AN29jM8s…pXGrJ9To AXvCVbr3…oeThyAFx AJyXeqnU…mRQ689ZH

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.

1.444 × 10⁹⁴(95-digit number)

14444053607613355914…23496871122732062079

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

1.444 × 10⁹⁴(95-digit number)

14444053607613355914…23496871122732062079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.444 × 10⁹⁴(95-digit number)

14444053607613355914…23496871122732062081

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

2.888 × 10⁹⁴(95-digit number)

28888107215226711828…46993742245464124159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.888 × 10⁹⁴(95-digit number)

28888107215226711828…46993742245464124161

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

5.777 × 10⁹⁴(95-digit number)

57776214430453423657…93987484490928248319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.777 × 10⁹⁴(95-digit number)

57776214430453423657…93987484490928248321

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

1.155 × 10⁹⁵(96-digit number)

11555242886090684731…87974968981856496639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.155 × 10⁹⁵(96-digit number)

11555242886090684731…87974968981856496641

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

2.311 × 10⁹⁵(96-digit number)

23110485772181369462…75949937963712993279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.311 × 10⁹⁵(96-digit number)

23110485772181369462…75949937963712993281

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

4.622 × 10⁹⁵(96-digit number)

46220971544362738925…51899875927425986559

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 #2,823,970

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