Block #4,061,964

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2021, 5:13:20 AM · Difficulty 10.8053 · 2,763,564 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

655dcdbf7c1575b1fe11c2d1a85f18c9ce994538a50af918aa22a0fc59d6a0bd

View on Chainz ↗

Height

#4,061,964

Difficulty

10.805281

Transactions

Size

1.11 KB

Version

Bits

0ace26e5

Nonce

568,678,537

Timestamp

2/2/2021, 5:13:20 AM

Confirmations

2,763,564

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMz Visit pool ↗

Merkle Root

b7af20acdbfadf5fa7025ca959bd166e6bac0aec8150c00b157cb2cfff8cbc3e

Transactions (4)

Coinbase336fd6a7f8d00c…c8c0aa948f6acd

1 in → 1 out8.5800 XPM110 B

AXfJqzUb…HXeXmjMz

4f65f6cb9b8981…5074dcf31639f1

2 in → 2 out13.0787 XPM340 B

Ab6uYUja…EseWVMwa ASiq2qtK…VMhmk7yL

b73e986dfe282a…222763da84301a

1 in → 2 out4.3975 XPM226 B

ASiq2qtK…VMhmk7yL AVh3Lahy…hjYBxwTt

db7c840c177e31…eef99c31c37f9a

2 in → 2 out4.0744 XPM374 B

AQvoeGK8…yd72tRVu ASiq2qtK…VMhmk7yL

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.

1.366 × 10⁹⁸(99-digit number)

13666967968396732637…25673936281609175039

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

1.366 × 10⁹⁸(99-digit number)

13666967968396732637…25673936281609175039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.366 × 10⁹⁸(99-digit number)

13666967968396732637…25673936281609175041

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

2.733 × 10⁹⁸(99-digit number)

27333935936793465275…51347872563218350079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.733 × 10⁹⁸(99-digit number)

27333935936793465275…51347872563218350081

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

5.466 × 10⁹⁸(99-digit number)

54667871873586930550…02695745126436700159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.466 × 10⁹⁸(99-digit number)

54667871873586930550…02695745126436700161

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

1.093 × 10⁹⁹(100-digit number)

10933574374717386110…05391490252873400319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.093 × 10⁹⁹(100-digit number)

10933574374717386110…05391490252873400321

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

2.186 × 10⁹⁹(100-digit number)

21867148749434772220…10782980505746800639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.186 × 10⁹⁹(100-digit number)

21867148749434772220…10782980505746800641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #4,061,964

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