Block #2,649,800

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/5/2018, 12:44:35 PM · Difficulty 11.7623 · 4,194,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3369bba0b8788f5e3cfa058896e9e7afa5ad4fe941e19ccd462f5ebe030424e9

View on Chainz ↗

Height

#2,649,800

Difficulty

11.762317

Transactions

Size

653 B

Version

Bits

0bc32732

Nonce

739,163,670

Timestamp

5/5/2018, 12:44:35 PM

Confirmations

4,194,198

Mined by

⛏️ P2SHAR5beMuF4QqgqcMPTKwqtzpPcru4PmYwGA

Merkle Root

ddf5547975efbc629ea08ecd69aec912a702cc97c7a65d806c28c044355bb315

Transactions (3)

Coinbase74d2d42fa2861c…9cab75ded72aeb

1 in → 1 out7.2400 XPM110 B

AR5beMuF…u4PmYwGA

f58ba2eecb7e3a…39099260f984e4

1 in → 2 out63.3644 XPM226 B

AdBfVwbp…JCfxUFD9 AdKgVFDC…t9aARSxj

b6e466f9079cd6…ec6be2e1655d54

1 in → 2 out20.1634 XPM227 B

AQRC1xnL…PW6njv6j AU4nnWBV…RU8JitPW

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.

2.530 × 10⁹⁴(95-digit number)

25308305012626037722…14601097935974370319

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

2.530 × 10⁹⁴(95-digit number)

25308305012626037722…14601097935974370319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.530 × 10⁹⁴(95-digit number)

25308305012626037722…14601097935974370321

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

5.061 × 10⁹⁴(95-digit number)

50616610025252075445…29202195871948740639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.061 × 10⁹⁴(95-digit number)

50616610025252075445…29202195871948740641

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

1.012 × 10⁹⁵(96-digit number)

10123322005050415089…58404391743897481279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.012 × 10⁹⁵(96-digit number)

10123322005050415089…58404391743897481281

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

2.024 × 10⁹⁵(96-digit number)

20246644010100830178…16808783487794962559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.024 × 10⁹⁵(96-digit number)

20246644010100830178…16808783487794962561

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

4.049 × 10⁹⁵(96-digit number)

40493288020201660356…33617566975589925119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.049 × 10⁹⁵(96-digit number)

40493288020201660356…33617566975589925121

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

8.098 × 10⁹⁵(96-digit number)

80986576040403320712…67235133951179850239

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 #2,649,800

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