Block #710,909

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2014, 12:07:51 PM · Difficulty 10.9563 · 6,097,060 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6dd55551a27dc40b28b2c90a81c9c76f7c44885741060e1414bb44c361600602

View on Chainz ↗

Height

#710,909

Difficulty

10.956323

Transactions

Size

1.15 KB

Version

Bits

0af4d194

Nonce

468,361,075

Timestamp

9/7/2014, 12:07:51 PM

Confirmations

6,097,060

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8b76f8ef24916bab4e443181e739ba506630dcadc50bb6f384cb5667191166e1

Transactions (4)

Coinbasea2328f91eb172c…49cbd2ad2cc7c5

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

ab177bed3082bd…f5aa9ddc1e8ef9

2 in → 2 out10.0608 XPM374 B

AbJHodB8…FhkrfFAY AJzjuYh3…ndhqFVng

3c380b7cea1cd0…ac6de6cb155d78

1 in → 2 out2.5847 XPM225 B

AeKNrjNj…1NEq95Ta ARJQsNEx…UvYvuSPW

09cada6306b25b…3de805b8de7578

2 in → 2 out2.4459 XPM375 B

AQGo42j5…hasj1Geg AaaFSc4c…DXKbuH3u

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.

4.290 × 10⁹⁶(97-digit number)

42908260821643579785…04967904400075980799

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

4.290 × 10⁹⁶(97-digit number)

42908260821643579785…04967904400075980799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.290 × 10⁹⁶(97-digit number)

42908260821643579785…04967904400075980801

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

8.581 × 10⁹⁶(97-digit number)

85816521643287159570…09935808800151961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.581 × 10⁹⁶(97-digit number)

85816521643287159570…09935808800151961601

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

1.716 × 10⁹⁷(98-digit number)

17163304328657431914…19871617600303923199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.716 × 10⁹⁷(98-digit number)

17163304328657431914…19871617600303923201

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

3.432 × 10⁹⁷(98-digit number)

34326608657314863828…39743235200607846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.432 × 10⁹⁷(98-digit number)

34326608657314863828…39743235200607846401

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

6.865 × 10⁹⁷(98-digit number)

68653217314629727656…79486470401215692799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.865 × 10⁹⁷(98-digit number)

68653217314629727656…79486470401215692801

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 #710,909

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