Block #1,268,868

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/6/2015, 2:05:17 AM · Difficulty 10.8165 · 5,558,094 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aec0412d3d4dc1d2cb2912ee2e1f7f8ae3081044c084a6aacacfc2312802670d

View on Chainz ↗

Height

#1,268,868

Difficulty

10.816487

Transactions

Size

1.55 KB

Version

Bits

0ad10544

Nonce

67,047,197

Timestamp

10/6/2015, 2:05:17 AM

Confirmations

5,558,094

Mined by

⛏️ P2SHAUuVdYdDsmLPhTXodgnRJYdjXGjFt4mrzQ

Merkle Root

c56bf5fa7a026fc41e155da48d08972415997897d249330372307a0e59827916

Transactions (5)

Coinbasef5d21a09fe4e1c…e08f3a5481549b

1 in → 1 out8.5700 XPM109 B

AUuVdYdD…jFt4mrzQ

a8b0f9d9e24e42…a22cddfe8cf92b

2 in → 2 out12.0685 XPM374 B

AHQCtY5K…UTBfYGxD ATgtCueY…YrBJEqDV

9bed4371bfb096…54375add421503

1 in → 12 out58.8716 XPM566 B

AZMoCniT…jKNKec56 AdNsYf3e…oT7bWNLb AFqAiWtG…JNZAjpHt Af2XA3jy…fRwaFg32 AWhHG3cs…Qkg16jh4

52a1c0c03213f9…09135a71f6caf6

1 in → 2 out6.3699 XPM226 B

AV56Gwjd…u67yDWM1 AJXD79Mh…8Qg7XE3E

db400f96c76b51…76cd7b634b922d

1 in → 2 out1.1225 XPM226 B

AXrTw46X…e1dGvSFf AcYtNTFx…H4PUS9qf

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.

8.428 × 10⁹⁵(96-digit number)

84280021826651707106…71718805012398899199

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

8.428 × 10⁹⁵(96-digit number)

84280021826651707106…71718805012398899199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.428 × 10⁹⁵(96-digit number)

84280021826651707106…71718805012398899201

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

1.685 × 10⁹⁶(97-digit number)

16856004365330341421…43437610024797798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.685 × 10⁹⁶(97-digit number)

16856004365330341421…43437610024797798401

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

3.371 × 10⁹⁶(97-digit number)

33712008730660682842…86875220049595596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.371 × 10⁹⁶(97-digit number)

33712008730660682842…86875220049595596801

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

6.742 × 10⁹⁶(97-digit number)

67424017461321365684…73750440099191193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.742 × 10⁹⁶(97-digit number)

67424017461321365684…73750440099191193601

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

1.348 × 10⁹⁷(98-digit number)

13484803492264273136…47500880198382387199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.348 × 10⁹⁷(98-digit number)

13484803492264273136…47500880198382387201

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 #1,268,868

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