Block #940,890

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2015, 9:15:55 PM · Difficulty 10.9011 · 5,869,265 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2207db21d080b2a28d4ef773f742caf6888d1be5bb3e9a55896f99496530490

View on Chainz ↗

Height

#940,890

Difficulty

10.901064

Transactions

Size

1.81 KB

Version

Bits

0ae6ac1d

Nonce

268,928,222

Timestamp

2/17/2015, 9:15:55 PM

Confirmations

5,869,265

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

430d816d37d0b6a40cfbf31ebd2da9baf69a8ec5907318f1026575a639e9630e

Transactions (5)

Coinbase9e33d8ca38e4a6…bff9bf60d0dc26

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

bdb7c3be5757c1…7ee019cf6663bc

5 in → 2 out141.1998 XPM817 B

AHqAhJKY…jC8vs5ud AHqP4BxH…TnuNRqsJ

e5396df7d7d0e0…2a5c7f2a8f0a98

2 in → 2 out12.0408 XPM375 B

AS8BK7MW…EzXkZrfL ATDzT9Qg…xPgwgjb1

2e4c63f83af634…5f5820e05a1404

1 in → 2 out7.8626 XPM227 B

AN2wNgdb…MrT8DcM4 AHRoBSh4…BSVTQ36Q

e3ffbaf169db38…5dce857e230a78

1 in → 2 out2.3357 XPM226 B

ALamExWH…te7UsbHr Ae7YXEyn…hnSYZsCr

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.

4.145 × 10⁹⁸(99-digit number)

41452930202835514394…47236046053430927359

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

4.145 × 10⁹⁸(99-digit number)

41452930202835514394…47236046053430927359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.145 × 10⁹⁸(99-digit number)

41452930202835514394…47236046053430927361

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

8.290 × 10⁹⁸(99-digit number)

82905860405671028788…94472092106861854719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.290 × 10⁹⁸(99-digit number)

82905860405671028788…94472092106861854721

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

1.658 × 10⁹⁹(100-digit number)

16581172081134205757…88944184213723709439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.658 × 10⁹⁹(100-digit number)

16581172081134205757…88944184213723709441

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

3.316 × 10⁹⁹(100-digit number)

33162344162268411515…77888368427447418879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.316 × 10⁹⁹(100-digit number)

33162344162268411515…77888368427447418881

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

6.632 × 10⁹⁹(100-digit number)

66324688324536823030…55776736854894837759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.632 × 10⁹⁹(100-digit number)

66324688324536823030…55776736854894837761

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 #940,890

Cookie Preferences