Block #2,858,125

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/28/2018, 7:21:33 AM · Difficulty 11.6812 · 3,983,208 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2345ba11e672b1c5ae5fdf01752cb59ecc5c87d2070197abc97c4ed874163b2

View on Chainz ↗

Height

#2,858,125

Difficulty

11.681213

Transactions

Size

1.30 KB

Version

Bits

0bae63f6

Nonce

1,145,218,570

Timestamp

9/28/2018, 7:21:33 AM

Confirmations

3,983,208

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

fb3d4dbb4847b4e441dc8fae90df9ff218352de1f137050319be406af0f2b1d0

Transactions (4)

Coinbased65751757fa0cf…d9374567c26d06

1 in → 1 out7.3500 XPM110 B

AUMQRepm…tAfKmdW1

afaf15662a9834…aa74461097b210

2 in → 2 out14.5700 XPM305 B

AU57vYZ7…MzSePeJt Aek7aQzY…4495YRvK

494c730d80f8ad…6ccfc1cddb0308

2 in → 2 out14.6500 XPM308 B

AUyZiWoC…FTgYtYHG AVTgQpTU…P2UwEkPT

83ac2a8c7fdf65…7f571e36350e68

3 in → 2 out11.0600 XPM522 B

AYnpgKTp…kDHJEMuE AGj2Qj2j…fCFHd8VB

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.

7.818 × 10⁹²(93-digit number)

78181316865387990311…81032215288800141199

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

7.818 × 10⁹²(93-digit number)

78181316865387990311…81032215288800141199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.818 × 10⁹²(93-digit number)

78181316865387990311…81032215288800141201

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

1.563 × 10⁹³(94-digit number)

15636263373077598062…62064430577600282399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.563 × 10⁹³(94-digit number)

15636263373077598062…62064430577600282401

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

3.127 × 10⁹³(94-digit number)

31272526746155196124…24128861155200564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.127 × 10⁹³(94-digit number)

31272526746155196124…24128861155200564801

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

6.254 × 10⁹³(94-digit number)

62545053492310392249…48257722310401129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.254 × 10⁹³(94-digit number)

62545053492310392249…48257722310401129601

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

1.250 × 10⁹⁴(95-digit number)

12509010698462078449…96515444620802259199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.250 × 10⁹⁴(95-digit number)

12509010698462078449…96515444620802259201

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

2.501 × 10⁹⁴(95-digit number)

25018021396924156899…93030889241604518399

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 #2,858,125

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