Block #2,884,931

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/17/2018, 11:23:52 AM · Difficulty 11.6278 · 3,951,781 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab32d87d288af33acfd0a84edbcca1afa228fabe29ebbdaa7144c938d624e2e5

View on Chainz ↗

Height

#2,884,931

Difficulty

11.627752

Transactions

Size

1.14 KB

Version

Bits

0ba0b459

Nonce

87,692,345

Timestamp

10/17/2018, 11:23:52 AM

Confirmations

3,951,781

Mined by

⛏️ P2SHAUhe1ZoY8286feLpGUnRRTKiNYDUGE8ae2

Merkle Root

513b5f40b2ca20def0d3341d079145212e1dda32a8b4af2ff6c6d11ce1a3eb8e

Transactions (2)

Coinbase85745bacb036b4…f1c2ab3eceaf27

1 in → 1 out7.4000 XPM109 B

AUhe1ZoY…DUGE8ae2

3b29f6dc1c6eb9…a389ee62790346

6 in → 2 out632.0591 XPM969 B

ATsX74ZL…1DwgaqFP AGFnDPgk…GEwU7aCf

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.

1.098 × 10⁹⁶(97-digit number)

10987129399337404077…76985503853301816319

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

1.098 × 10⁹⁶(97-digit number)

10987129399337404077…76985503853301816319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.098 × 10⁹⁶(97-digit number)

10987129399337404077…76985503853301816321

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

2.197 × 10⁹⁶(97-digit number)

21974258798674808155…53971007706603632639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.197 × 10⁹⁶(97-digit number)

21974258798674808155…53971007706603632641

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

4.394 × 10⁹⁶(97-digit number)

43948517597349616311…07942015413207265279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.394 × 10⁹⁶(97-digit number)

43948517597349616311…07942015413207265281

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

8.789 × 10⁹⁶(97-digit number)

87897035194699232623…15884030826414530559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.789 × 10⁹⁶(97-digit number)

87897035194699232623…15884030826414530561

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

1.757 × 10⁹⁷(98-digit number)

17579407038939846524…31768061652829061119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.757 × 10⁹⁷(98-digit number)

17579407038939846524…31768061652829061121

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

3.515 × 10⁹⁷(98-digit number)

35158814077879693049…63536123305658122239

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 #2,884,931

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