Block #415,912

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 1:40:13 AM · Difficulty 10.3993 · 6,394,852 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7d4779d0dca2344df016da01efa72b2f2a77bddb0e10f42f0291bbcbe27d8f5

View on Chainz ↗

Height

#415,912

Difficulty

10.399276

Transactions

Size

401 B

Version

Bits

0a6636f1

Nonce

10,067

Timestamp

2/23/2014, 1:40:13 AM

Confirmations

6,394,852

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b45914c9f466fb4fa2a085f535cbfb2af87a828ccfc7a4124fe2c9e7feda423c

Transactions (2)

Coinbase43be86376dd775…f851dff1b1f62d

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

6b84d4c27c4944…1820d74273c9f0

1 in → 1 out2.0308 XPM192 B

AFwD4q46…sxTWDQig

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.

8.839 × 10¹⁰⁰(101-digit number)

88399098780154068221…35949504254580044799

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

8.839 × 10¹⁰⁰(101-digit number)

88399098780154068221…35949504254580044799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.839 × 10¹⁰⁰(101-digit number)

88399098780154068221…35949504254580044801

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

1.767 × 10¹⁰¹(102-digit number)

17679819756030813644…71899008509160089599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.767 × 10¹⁰¹(102-digit number)

17679819756030813644…71899008509160089601

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

3.535 × 10¹⁰¹(102-digit number)

35359639512061627288…43798017018320179199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.535 × 10¹⁰¹(102-digit number)

35359639512061627288…43798017018320179201

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

7.071 × 10¹⁰¹(102-digit number)

70719279024123254577…87596034036640358399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.071 × 10¹⁰¹(102-digit number)

70719279024123254577…87596034036640358401

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

1.414 × 10¹⁰²(103-digit number)

14143855804824650915…75192068073280716799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.414 × 10¹⁰²(103-digit number)

14143855804824650915…75192068073280716801

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 #415,912

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