Block #945,279

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/21/2015, 12:38:08 AM · Difficulty 10.8986 · 5,880,437 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ac3e3ab66f131040d0d631578b52739d71f8178cdee9dd2d70d6efd93dcd400

View on Chainz ↗

Height

#945,279

Difficulty

10.898555

Transactions

Size

1.38 KB

Version

Bits

0ae607b2

Nonce

142,396,422

Timestamp

2/21/2015, 12:38:08 AM

Confirmations

5,880,437

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1383dda4a55ebaab27124f0d0568131226e6cbc4df589722d8b736a0a959a906

Transactions (5)

Coinbase1b3bde7df2eb3b…8d7bd20037e464

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

9832dc95bafd5e…5f7e3e09a76f21

1 in → 2 out8.3900 XPM226 B

APPFoVzV…TfiMApne AHRoBSh4…BSVTQ36Q

ed350197da9e1a…71c17dd2a908c2

1 in → 2 out8.3900 XPM226 B

APaYVt8e…rPF99zd2 AWDHwPB6…4366Y8Df

f2d6e8f114586b…14b2955a196284

1 in → 2 out8.3900 XPM226 B

AMCoAx9g…4S2GXwvC AbAzfBrm…3HxwMzDi

6b2c7e1cc1819b…a50b6701dcf52d

3 in → 2 out10.8637 XPM522 B

ATDzT9Qg…xPgwgjb1 ARGGWLcv…e2BVrKkm

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.

4.820 × 10⁹⁹(100-digit number)

48204629678992667191…48146229353381887999

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

4.820 × 10⁹⁹(100-digit number)

48204629678992667191…48146229353381887999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.820 × 10⁹⁹(100-digit number)

48204629678992667191…48146229353381888001

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

9.640 × 10⁹⁹(100-digit number)

96409259357985334383…96292458706763775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.640 × 10⁹⁹(100-digit number)

96409259357985334383…96292458706763776001

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

1.928 × 10¹⁰⁰(101-digit number)

19281851871597066876…92584917413527551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.928 × 10¹⁰⁰(101-digit number)

19281851871597066876…92584917413527552001

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

3.856 × 10¹⁰⁰(101-digit number)

38563703743194133753…85169834827055103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.856 × 10¹⁰⁰(101-digit number)

38563703743194133753…85169834827055104001

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

7.712 × 10¹⁰⁰(101-digit number)

77127407486388267506…70339669654110207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.712 × 10¹⁰⁰(101-digit number)

77127407486388267506…70339669654110208001

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 #945,279

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