Block #315,600

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 2:35:58 PM · Difficulty 10.1083 · 6,509,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b653333c3262c12c8e33ac087969bf2083f4db0e339f7663f3b37cf04ac40145

View on Chainz ↗

Height

#315,600

Difficulty

10.108306

Transactions

Size

877 B

Version

Bits

0a1bb9f0

Nonce

64,545

Timestamp

12/16/2013, 2:35:58 PM

Confirmations

6,509,052

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

398a1b6cfcfd048351fde1a4248016532b6528ff4293f965fb1a120e876ec553

Transactions (4)

Coinbased951a410fcf0f8…7eafc8849933c9

1 in → 1 out9.8000 XPM110 B

AeKNrjNj…1NEq95Ta

808687710404a6…7c1a812ca6bd1a

1 in → 2 out9.9800 XPM226 B

AdDXUU3u…xQjSdYKw AN8RKugL…d6m3McZX

dd969193b49417…b62a26900d5e1a

1 in → 2 out9.9800 XPM226 B

AeuUdzZu…SFapvjeD AW8hy3g7…12Ev2HJk

622c5f1f8545ab…ade424f626335d

1 in → 2 out9.9800 XPM226 B

AaNaUXom…4ancKyQw AJdX5B5v…EuN9AfAW

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.

4.415 × 10⁹²(93-digit number)

44159906989204274218…72592845569489734719

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

4.415 × 10⁹²(93-digit number)

44159906989204274218…72592845569489734719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.415 × 10⁹²(93-digit number)

44159906989204274218…72592845569489734721

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

8.831 × 10⁹²(93-digit number)

88319813978408548437…45185691138979469439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.831 × 10⁹²(93-digit number)

88319813978408548437…45185691138979469441

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

1.766 × 10⁹³(94-digit number)

17663962795681709687…90371382277958938879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.766 × 10⁹³(94-digit number)

17663962795681709687…90371382277958938881

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

3.532 × 10⁹³(94-digit number)

35327925591363419374…80742764555917877759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.532 × 10⁹³(94-digit number)

35327925591363419374…80742764555917877761

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

7.065 × 10⁹³(94-digit number)

70655851182726838749…61485529111835755519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.065 × 10⁹³(94-digit number)

70655851182726838749…61485529111835755521

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 #315,600

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