Block #929,140

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/9/2015, 2:16:15 PM · Difficulty 10.9039 · 5,876,915 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3ce3583601730cf477425cd3caf1414bdb0ef5b77536a95fbee6e93296b491a

View on Chainz ↗

Height

#929,140

Difficulty

10.903910

Transactions

Size

1.01 KB

Version

Bits

0ae766ac

Nonce

76,393,439

Timestamp

2/9/2015, 2:16:15 PM

Confirmations

5,876,915

Mined by

⛏️ P2SHAZAGMrjC5GCnMPrS2Y4qpVEK8ifxunP9zo

Merkle Root

33e474f60d9c21eeb9865988814be7cdb4b9fdde77a8e3f8d8e8c2f72d08594f

Transactions (5)

Coinbasea61261665ef5d3…e2abeb85bdebe2

1 in → 1 out8.4400 XPM110 B

AZAGMrjC…fxunP9zo

c53a7fb51781b0…677eb16c182c18

1 in → 1 out8.3800 XPM159 B

AekLq4Sw…ueWMfyir

198b27a5bf8c7e…957ddc882c57b1

1 in → 2 out3094.2300 XPM226 B

AdAdeeLh…NPBrzDYf AZzZCvZu…CS35xtcu

b519178d675d2c…4d6512b75b53ac

1 in → 2 out3090.2200 XPM226 B

AaVTw9zG…aTSUbRK4 AdGFnV3a…o6n2zX3x

aff00f4980d1f5…c719295beb9239

1 in → 2 out3086.2100 XPM226 B

AQk8UUJb…DWzXo5AT ATLVMaGk…YAMVKG23

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.

1.698 × 10⁹⁴(95-digit number)

16980520246473430225…14090889401509854359

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

1.698 × 10⁹⁴(95-digit number)

16980520246473430225…14090889401509854359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.698 × 10⁹⁴(95-digit number)

16980520246473430225…14090889401509854361

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

3.396 × 10⁹⁴(95-digit number)

33961040492946860451…28181778803019708719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.396 × 10⁹⁴(95-digit number)

33961040492946860451…28181778803019708721

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

6.792 × 10⁹⁴(95-digit number)

67922080985893720902…56363557606039417439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.792 × 10⁹⁴(95-digit number)

67922080985893720902…56363557606039417441

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

1.358 × 10⁹⁵(96-digit number)

13584416197178744180…12727115212078834879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.358 × 10⁹⁵(96-digit number)

13584416197178744180…12727115212078834881

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

2.716 × 10⁹⁵(96-digit number)

27168832394357488361…25454230424157669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.716 × 10⁹⁵(96-digit number)

27168832394357488361…25454230424157669761

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

5.433 × 10⁹⁵(96-digit number)

54337664788714976722…50908460848315339519

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