Block #914,441

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2015, 9:14:44 AM · Difficulty 10.9274 · 5,891,475 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44013c328251026ef51ba1534b16591af17497ee62ee3da4169930c5a7f1a96e

View on Chainz ↗

Height

#914,441

Difficulty

10.927420

Transactions

Size

869 B

Version

Bits

0aed6b6d

Nonce

631,411,347

Timestamp

1/29/2015, 9:14:44 AM

Confirmations

5,891,475

Mined by

⛏️ P2SHAFnwMJFegdHhcSKxqYCsidLA4rLHj6RZCJ

Merkle Root

f145b61325f70641f8966bd6d3a21047e557a0aab62e1e659d7aee97c73a1437

Transactions (2)

Coinbasebe58e718468ee6…bde4490e2c8ac4

1 in → 1 out8.3700 XPM109 B

AFnwMJFe…LHj6RZCJ

c20d923579d743…0aae61d363ab2a

4 in → 2 out57.7378 XPM670 B

AYbQUuPy…ngBocWSr AXZ15i9u…YGRCff1v

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.

1.310 × 10⁹⁵(96-digit number)

13107179641065856952…53815163977205104639

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

1.310 × 10⁹⁵(96-digit number)

13107179641065856952…53815163977205104639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.310 × 10⁹⁵(96-digit number)

13107179641065856952…53815163977205104641

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

2.621 × 10⁹⁵(96-digit number)

26214359282131713905…07630327954410209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.621 × 10⁹⁵(96-digit number)

26214359282131713905…07630327954410209281

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

5.242 × 10⁹⁵(96-digit number)

52428718564263427811…15260655908820418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.242 × 10⁹⁵(96-digit number)

52428718564263427811…15260655908820418561

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

1.048 × 10⁹⁶(97-digit number)

10485743712852685562…30521311817640837119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.048 × 10⁹⁶(97-digit number)

10485743712852685562…30521311817640837121

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

2.097 × 10⁹⁶(97-digit number)

20971487425705371124…61042623635281674239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.097 × 10⁹⁶(97-digit number)

20971487425705371124…61042623635281674241

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