Block #690,481

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/24/2014, 9:12:29 AM · Difficulty 10.9548 · 6,125,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

176d7daac8b9fa78018ed50cb2d3c7626e55c0f86a9d819b7d487c91655f6ed9

View on Chainz ↗

Height

#690,481

Difficulty

10.954812

Transactions

Size

1.52 KB

Version

Bits

0af46e96

Nonce

238,127,787

Timestamp

8/24/2014, 9:12:29 AM

Confirmations

6,125,566

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ed3d2f3e4ffb382faafd71d4d00c1744d790fe5265ae7c1b5df3c15a32012564

Transactions (5)

Coinbase17e3e4b64b3cbd…429716f52d2c61

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

1d293dd84936f5…9d9ecbc45769d9

1 in → 2 out8.3000 XPM226 B

AYU1Ynxb…6LNs2ZYM AU9yPGJN…yjXMZG8S

f99f8151dc92fc…88784a6f02cda7

1 in → 2 out8.3000 XPM226 B

APa42Y5u…RRnPo7bS APVdfbfH…1FUmTWCf

d75f1af7e2af1f…ed9305499fa6c2

3 in → 2 out24.9400 XPM523 B

AajXbSHz…BNvgBxeX APZZjcPT…mEjtCRTo

e2852559593ff1…3d6ade1918a7aa

2 in → 2 out0.6656 XPM374 B

AbwXaLqN…z6HW1wCk ARBaHyDg…2Ed87FaU

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.

9.628 × 10⁹⁵(96-digit number)

96281696864409371412…74506995187250679039

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

9.628 × 10⁹⁵(96-digit number)

96281696864409371412…74506995187250679039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.628 × 10⁹⁵(96-digit number)

96281696864409371412…74506995187250679041

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

1.925 × 10⁹⁶(97-digit number)

19256339372881874282…49013990374501358079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.925 × 10⁹⁶(97-digit number)

19256339372881874282…49013990374501358081

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

3.851 × 10⁹⁶(97-digit number)

38512678745763748564…98027980749002716159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.851 × 10⁹⁶(97-digit number)

38512678745763748564…98027980749002716161

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

7.702 × 10⁹⁶(97-digit number)

77025357491527497129…96055961498005432319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.702 × 10⁹⁶(97-digit number)

77025357491527497129…96055961498005432321

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

1.540 × 10⁹⁷(98-digit number)

15405071498305499425…92111922996010864639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.540 × 10⁹⁷(98-digit number)

15405071498305499425…92111922996010864641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.081 × 10⁹⁷(98-digit number)

30810142996610998851…84223845992021729279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #690,481

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