Block #959,751

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2015, 10:40:51 AM · Difficulty 10.8878 · 5,848,064 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

660c6a1a90b3ea713b64a397aad43809b0b978dd5f1fc0d6f4e91ee07953c468

View on Chainz ↗

Height

#959,751

Difficulty

10.887765

Transactions

Size

1.38 KB

Version

Bits

0ae34493

Nonce

1,072,471,896

Timestamp

3/3/2015, 10:40:51 AM

Confirmations

5,848,064

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

27ad8e4b611b01b48bc43dd31a07b23edb8cf0105009e580f902ea1db79f2c62

Transactions (5)

Coinbased7fe8758c5c3a3…fe82640ecd5f62

1 in → 1 out8.4600 XPM116 B

ANSXnLY2…Sd25TjkD

5a8fc46c233cb5…985851f89b33db

2 in → 2 out11.8281 XPM374 B

ALrz72BF…tipQBftJ ATDzT9Qg…xPgwgjb1

c9e9b1aebe6871…db4d1ded402c8d

2 in → 2 out12.5464 XPM375 B

ANNBoEaA…o6TzGWqw AXmTXVEF…Gz7WUwcB

fa2b7f557ab4cc…95951551f74c32

1 in → 2 out5.6894 XPM227 B

APUe52is…bKm6o26Y ANfmUrFA…kVSzdPqM

b318f2d042592d…9b7cd2f5743e84

1 in → 2 out5.5754 XPM227 B

ARpjHv1k…4F9NvuWN ANjL6oyD…ciy7GtU4

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.

1.693 × 10⁹⁶(97-digit number)

16932154764086278643…24204964175377439679

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

1.693 × 10⁹⁶(97-digit number)

16932154764086278643…24204964175377439679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.693 × 10⁹⁶(97-digit number)

16932154764086278643…24204964175377439681

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

3.386 × 10⁹⁶(97-digit number)

33864309528172557287…48409928350754879359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.386 × 10⁹⁶(97-digit number)

33864309528172557287…48409928350754879361

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

6.772 × 10⁹⁶(97-digit number)

67728619056345114574…96819856701509758719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.772 × 10⁹⁶(97-digit number)

67728619056345114574…96819856701509758721

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

1.354 × 10⁹⁷(98-digit number)

13545723811269022914…93639713403019517439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.354 × 10⁹⁷(98-digit number)

13545723811269022914…93639713403019517441

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

2.709 × 10⁹⁷(98-digit number)

27091447622538045829…87279426806039034879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.709 × 10⁹⁷(98-digit number)

27091447622538045829…87279426806039034881

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 #959,751

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