Block #314,411

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2013, 10:52:37 PM · Difficulty 10.0623 · 6,512,158 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7dc6386179bf6f93bbd3031d170e182babc7db91d65f12e3077bf9b23ba0e2c6

View on Chainz ↗

Height

#314,411

Difficulty

10.062260

Transactions

Size

1.08 KB

Version

Bits

0a0ff04c

Nonce

37,560

Timestamp

12/15/2013, 10:52:37 PM

Confirmations

6,512,158

Mined by

⛏️ +aR2Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

bf713bbe90f772190ab897eb05f0bf522a5c21503ee2f9da9f5968f2c55a0068

Transactions (1)

Coinbasebf713bbe90f772…5968f2c55a0068

1 in → 28 out9.8400 XPM1015 B

Aac9Hjdg…P4ktypc3 AbtgNzNb…9Atvu81w AYtDvcGs…VuAcA7m7 AXLMLPqA…tXRY1rrP AJ9QW1VP…GmAJhvhc

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.

1.246 × 10¹⁰²(103-digit number)

12463356175321943701…04545522190799911679

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

1.246 × 10¹⁰²(103-digit number)

12463356175321943701…04545522190799911679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.246 × 10¹⁰²(103-digit number)

12463356175321943701…04545522190799911681

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

2.492 × 10¹⁰²(103-digit number)

24926712350643887402…09091044381599823359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.492 × 10¹⁰²(103-digit number)

24926712350643887402…09091044381599823361

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

4.985 × 10¹⁰²(103-digit number)

49853424701287774805…18182088763199646719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.985 × 10¹⁰²(103-digit number)

49853424701287774805…18182088763199646721

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

9.970 × 10¹⁰²(103-digit number)

99706849402575549610…36364177526399293439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.970 × 10¹⁰²(103-digit number)

99706849402575549610…36364177526399293441

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

1.994 × 10¹⁰³(104-digit number)

19941369880515109922…72728355052798586879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.994 × 10¹⁰³(104-digit number)

19941369880515109922…72728355052798586881

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 #314,411

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