Block #310,603

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 3:45:21 AM · Difficulty 9.9952 · 6,497,368 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70ae3b515fb80e3add27dced9ad27cbb2ef79ac19f81f5a559f6dc7781e3db5f

View on Chainz ↗

Height

#310,603

Difficulty

9.995237

Transactions

Size

12.33 KB

Version

Bits

09fec7e2

Nonce

7,250

Timestamp

12/14/2013, 3:45:21 AM

Confirmations

6,497,368

Mined by

⛏️ KaRCAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

0b328540a6682b63b02f0d91058a763769888acc34a7f4308d2aad55595ea1e1

Transactions (4)

Coinbase9dc72426e41685…a4152f65d8c089

1 in → 30 out9.9650 XPM1.06 KB

Aac9Hjdg…P4ktypc3 AXmS7tZu…11YypHLP AMiJebLB…rK2iN8iS AYcLTeXR…bscgPops AHuJ9wYh…BGmgHrKZ

7887c06d4443b6…f880579de79d88

67 in → 2 out21.0638 XPM9.77 KB

ATrZibkv…b2FhWcnZ AQcXWDVh…TvuJC1iS

c529b4829c3cc7…2897fd500899e6

8 in → 1 out2.0520 XPM1.20 KB

AGM5kDMt…t9n1kxWc

b30cd63507dc79…6325b0060d237a

1 in → 2 out2.2740 XPM226 B

AYGU135Q…mAKoEuxY AaAjWe4s…ZaFKy9nF

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.

4.379 × 10⁹³(94-digit number)

43796127447480523828…81483621621308544999

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

4.379 × 10⁹³(94-digit number)

43796127447480523828…81483621621308544999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.379 × 10⁹³(94-digit number)

43796127447480523828…81483621621308545001

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

8.759 × 10⁹³(94-digit number)

87592254894961047656…62967243242617089999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.759 × 10⁹³(94-digit number)

87592254894961047656…62967243242617090001

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

1.751 × 10⁹⁴(95-digit number)

17518450978992209531…25934486485234179999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.751 × 10⁹⁴(95-digit number)

17518450978992209531…25934486485234180001

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

3.503 × 10⁹⁴(95-digit number)

35036901957984419062…51868972970468359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.503 × 10⁹⁴(95-digit number)

35036901957984419062…51868972970468360001

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

7.007 × 10⁹⁴(95-digit number)

70073803915968838125…03737945940936719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.007 × 10⁹⁴(95-digit number)

70073803915968838125…03737945940936720001

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 #310,603

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