Block #603,269

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/26/2014, 10:04:45 PM · Difficulty 10.9123 · 6,223,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b6454f65b22183dc90ca8612603d111892239591ce2e920c958d44a6185d2ef

View on Chainz ↗

Height

#603,269

Difficulty

10.912277

Transactions

Size

434 B

Version

Bits

0ae98b00

Nonce

249,653,367

Timestamp

6/26/2014, 10:04:45 PM

Confirmations

6,223,727

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1ef2c5d1ed83dae1bb09a42a451acfa6e814bb24fe0cc7780b9afde9c11d700f

Transactions (2)

Coinbase98243e0f1b16d9…0d102ddec95aed

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

b59b837f572566…cb025ef3c8f5ed

1 in → 2 out5.2262 XPM226 B

AeKNrjNj…1NEq95Ta ARyHReP1…RCDqPuwD

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.

4.790 × 10⁹⁸(99-digit number)

47902482012075358149…33526489027788172799

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

4.790 × 10⁹⁸(99-digit number)

47902482012075358149…33526489027788172799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.790 × 10⁹⁸(99-digit number)

47902482012075358149…33526489027788172801

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

9.580 × 10⁹⁸(99-digit number)

95804964024150716298…67052978055576345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.580 × 10⁹⁸(99-digit number)

95804964024150716298…67052978055576345601

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

1.916 × 10⁹⁹(100-digit number)

19160992804830143259…34105956111152691199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.916 × 10⁹⁹(100-digit number)

19160992804830143259…34105956111152691201

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

3.832 × 10⁹⁹(100-digit number)

38321985609660286519…68211912222305382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.832 × 10⁹⁹(100-digit number)

38321985609660286519…68211912222305382401

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

7.664 × 10⁹⁹(100-digit number)

76643971219320573038…36423824444610764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.664 × 10⁹⁹(100-digit number)

76643971219320573038…36423824444610764801

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 #603,269

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