Block #725,298

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/17/2014, 5:14:54 AM · Difficulty 10.9601 · 6,090,581 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c61aeff8dc96f5de614737c3b1e23086f84446ed2a2371da2bdee64abe059d64

View on Chainz ↗

Height

#725,298

Difficulty

10.960061

Transactions

Size

593 B

Version

Bits

0af5c68a

Nonce

302,826,192

Timestamp

9/17/2014, 5:14:54 AM

Confirmations

6,090,581

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d1bf7697802e03bab1c49393a0ba1b53014dffd0ec64f69745a25ab1f42d6865

Transactions (3)

Coinbaseaf5dfbd4e8cd0f…c107fb402fed14

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

32b9bd51cebbd5…be11c7f1950f90

1 in → 1 out8.3100 XPM159 B

AekLq4Sw…ueWMfyir

f36bdb85575d9d…94c23dff8817a5

1 in → 2 out7.7887 XPM227 B

APVdfbfH…1FUmTWCf ASNdUmdW…bBCrXSoK

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.

3.075 × 10⁹⁷(98-digit number)

30751270082407450284…09248204505692564479

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

3.075 × 10⁹⁷(98-digit number)

30751270082407450284…09248204505692564479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.075 × 10⁹⁷(98-digit number)

30751270082407450284…09248204505692564481

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

6.150 × 10⁹⁷(98-digit number)

61502540164814900569…18496409011385128959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.150 × 10⁹⁷(98-digit number)

61502540164814900569…18496409011385128961

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

1.230 × 10⁹⁸(99-digit number)

12300508032962980113…36992818022770257919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.230 × 10⁹⁸(99-digit number)

12300508032962980113…36992818022770257921

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

2.460 × 10⁹⁸(99-digit number)

24601016065925960227…73985636045540515839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.460 × 10⁹⁸(99-digit number)

24601016065925960227…73985636045540515841

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

4.920 × 10⁹⁸(99-digit number)

49202032131851920455…47971272091081031679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.920 × 10⁹⁸(99-digit number)

49202032131851920455…47971272091081031681

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 #725,298

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