Block #2,855,369

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 9/26/2018, 4:07:28 AM · Difficulty 11.7007 · 3,988,637 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8c26a2f56ae9f2306d35689d80af942feeff6ba0906d008cc2ec2c668ceec66

View on Chainz ↗

Height

#2,855,369

Difficulty

11.700659

Transactions

Size

1.60 KB

Version

Bits

0bb35e5c

Nonce

303,493,591

Timestamp

9/26/2018, 4:07:28 AM

Confirmations

3,988,637

Mined by

⛏️ P2SHASMnPKsVy5u4MjAEFxDafqz4XARCh3tu6d

Merkle Root

beba46c547957152fcf1b1de8d6fb22fe27c1ebb663a7edf6f74c1d323ce1bb0

Transactions (5)

Coinbasebc20c88126ffd8…54ef45c49cd307

1 in → 1 out7.3300 XPM110 B

ASMnPKsV…RCh3tu6d

ec643817c4693e…6f1b39f4509058

2 in → 2 out14.7700 XPM307 B

ANEq6Gdi…Pbk4HtRv ATNA8L43…1KwDgfHB

643ef6d215b08e…556194735dc4eb

2 in → 2 out14.5100 XPM306 B

AXPKqszN…D5bxhV7x APVKWthF…PMMxwRoz

16c596d46b1849…e6718c825b54ba

2 in → 2 out14.5100 XPM307 B

AbEGQAeZ…xy9YA9Wc Aek7aQzY…4495YRvK

b677786ca41b5b…29121025b507af

3 in → 2 out13.7800 XPM522 B

AVwWU3EW…JtY7PqEe APVKWthF…PMMxwRoz

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.

2.818 × 10⁹⁶(97-digit number)

28187621479354378780…89062310236195235839

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

2.818 × 10⁹⁶(97-digit number)

28187621479354378780…89062310236195235839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.818 × 10⁹⁶(97-digit number)

28187621479354378780…89062310236195235841

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

5.637 × 10⁹⁶(97-digit number)

56375242958708757560…78124620472390471679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.637 × 10⁹⁶(97-digit number)

56375242958708757560…78124620472390471681

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

1.127 × 10⁹⁷(98-digit number)

11275048591741751512…56249240944780943359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.127 × 10⁹⁷(98-digit number)

11275048591741751512…56249240944780943361

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

2.255 × 10⁹⁷(98-digit number)

22550097183483503024…12498481889561886719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.255 × 10⁹⁷(98-digit number)

22550097183483503024…12498481889561886721

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

4.510 × 10⁹⁷(98-digit number)

45100194366967006048…24996963779123773439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.510 × 10⁹⁷(98-digit number)

45100194366967006048…24996963779123773441

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

9.020 × 10⁹⁷(98-digit number)

90200388733934012096…49993927558247546879

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

9.020 × 10⁹⁷(98-digit number)

90200388733934012096…49993927558247546881

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 #2,855,369

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