Block #306,864

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 7:13:30 AM · Difficulty 9.9940 · 6,508,126 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2f70f24ce3e5b3b76159d3253d8e39ec5aaf0a8be3ad203ae562b461742d975

View on Chainz ↗

Height

#306,864

Difficulty

9.993989

Transactions

Size

1.33 KB

Version

Bits

09fe7611

Nonce

12,148

Timestamp

12/12/2013, 7:13:30 AM

Confirmations

6,508,126

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5999e88177428b5425923f9f6ea7ae3b89f65a5eb510d4bc3fc3c314a6288baf

Transactions (5)

Coinbase06126b2099968a…41591ab1a902ea

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

8de38a1aa8066e…b7545991c2e983

3 in → 2 out15.1455 XPM523 B

AT5oTsET…Pi5H6raU ANtYikKx…mTYWDp2Z

6e1fa29841cc78…434c8683ca0cc7

1 in → 1 out3.1458 XPM192 B

AJdey1ZX…VsLUFHFg

d858c6a4de913c…b0dd64c356f445

1 in → 2 out3.4957 XPM226 B

AX96DALi…WqEU1Gm4 AcQcu1QN…1Kfnq2ya

c20cba82eade62…6107401b48e164

1 in → 2 out1.8649 XPM225 B

AU9PUUHV…8sLA1Ycb AWHqSsod…S114Gc1Y

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.

1.316 × 10⁹⁴(95-digit number)

13164676974751374320…72641683597627314399

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

1.316 × 10⁹⁴(95-digit number)

13164676974751374320…72641683597627314399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.316 × 10⁹⁴(95-digit number)

13164676974751374320…72641683597627314401

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

2.632 × 10⁹⁴(95-digit number)

26329353949502748641…45283367195254628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.632 × 10⁹⁴(95-digit number)

26329353949502748641…45283367195254628801

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

5.265 × 10⁹⁴(95-digit number)

52658707899005497282…90566734390509257599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.265 × 10⁹⁴(95-digit number)

52658707899005497282…90566734390509257601

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

1.053 × 10⁹⁵(96-digit number)

10531741579801099456…81133468781018515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.053 × 10⁹⁵(96-digit number)

10531741579801099456…81133468781018515201

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

2.106 × 10⁹⁵(96-digit number)

21063483159602198913…62266937562037030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.106 × 10⁹⁵(96-digit number)

21063483159602198913…62266937562037030401

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 #306,864

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