Block #3,485,020

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/21/2019, 5:35:52 AM · Difficulty 10.9789 · 3,354,195 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

312520d4b95549446dbe412e4a60d9c2156d3ae59593812d1b1797f3b43c5020

View on Chainz ↗

Height

#3,485,020

Difficulty

10.978901

Transactions

Size

4.25 KB

Version

Bits

0afa9940

Nonce

1,772,520,722

Timestamp

12/21/2019, 5:35:52 AM

Confirmations

3,354,195

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMz Visit pool ↗

Merkle Root

823281afd62b1aa8cb16a0c4abab7e26226dff9b233a1a6928715eb93456242f

Transactions (3)

Coinbasec17ffa69e73d94…3c6e232dc38de7

1 in → 1 out8.3300 XPM110 B

AXfJqzUb…HXeXmjMz

316ac353018ada…05f9eb121815ba

11 in → 2 out949.3199 XPM1.67 KB

AMJTarMU…jqYCgxNB AP2ikm3r…2qJRNrn6

1d0710f11e6681…a1158ec9747be0

16 in → 2 out1530.0000 XPM2.39 KB

AYJwRa68…qZK4EN8y AX3W6pJy…NwZ88svU

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.

7.400 × 10⁹⁴(95-digit number)

74008145482643587796…57953916880861126199

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

7.400 × 10⁹⁴(95-digit number)

74008145482643587796…57953916880861126199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.400 × 10⁹⁴(95-digit number)

74008145482643587796…57953916880861126201

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

1.480 × 10⁹⁵(96-digit number)

14801629096528717559…15907833761722252399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.480 × 10⁹⁵(96-digit number)

14801629096528717559…15907833761722252401

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

2.960 × 10⁹⁵(96-digit number)

29603258193057435118…31815667523444504799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.960 × 10⁹⁵(96-digit number)

29603258193057435118…31815667523444504801

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

5.920 × 10⁹⁵(96-digit number)

59206516386114870237…63631335046889009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.920 × 10⁹⁵(96-digit number)

59206516386114870237…63631335046889009601

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

1.184 × 10⁹⁶(97-digit number)

11841303277222974047…27262670093778019199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.184 × 10⁹⁶(97-digit number)

11841303277222974047…27262670093778019201

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

2.368 × 10⁹⁶(97-digit number)

23682606554445948094…54525340187556038399

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 #3,485,020

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