Block #296,978

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 8:26:50 AM · Difficulty 9.9918 · 6,506,626 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1574a895bcbfff568e2182117788acfc922a53d31c2d81e6437ba94a480f81be

View on Chainz ↗

Height

#296,978

Difficulty

9.991834

Transactions

Size

1.04 KB

Version

Bits

09fde8da

Nonce

79,622

Timestamp

12/6/2013, 8:26:50 AM

Confirmations

6,506,626

Mined by

⛏️ aRkAQyr8Lw3A4nTbkdHcAPqKiPptkhs4nt3Pn

Merkle Root

ebc0eeed681e21ae3e1248fcf51b07532b6f1fff319a6f5717df936b6cc9a91d

Transactions (1)

Coinbaseebc0eeed681e21…df936b6cc9a91d

1 in → 27 out10.0000 XPM981 B

AQyr8Lw3…hs4nt3Pn AUsTcddg…Z78ayoFz Abi6i7et…sYEvwaV9 ATC4q3RB…C1XVXAS3 AVnJZre9…7fQQrSqU

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.

1.986 × 10⁹¹(92-digit number)

19866850462530583414…37631344947953617599

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

1.986 × 10⁹¹(92-digit number)

19866850462530583414…37631344947953617599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.986 × 10⁹¹(92-digit number)

19866850462530583414…37631344947953617601

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

3.973 × 10⁹¹(92-digit number)

39733700925061166828…75262689895907235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.973 × 10⁹¹(92-digit number)

39733700925061166828…75262689895907235201

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

7.946 × 10⁹¹(92-digit number)

79467401850122333657…50525379791814470399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.946 × 10⁹¹(92-digit number)

79467401850122333657…50525379791814470401

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

1.589 × 10⁹²(93-digit number)

15893480370024466731…01050759583628940799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.589 × 10⁹²(93-digit number)

15893480370024466731…01050759583628940801

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

3.178 × 10⁹²(93-digit number)

31786960740048933462…02101519167257881599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.178 × 10⁹²(93-digit number)

31786960740048933462…02101519167257881601

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