Block #249,263

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 8:47:41 PM · Difficulty 9.9667 · 6,547,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4346bbe685b47be89f8fb8a8dfaa543f78d06c62b08ee727988adbcd37193432

View on Chainz ↗

Height

#249,263

Difficulty

9.966701

Transactions

Size

2.10 KB

Version

Bits

09f779b1

Nonce

3,627

Timestamp

11/7/2013, 8:47:41 PM

Confirmations

6,547,244

Mined by

⛏️ R{_AGaKkABVLDgiD9d9cgsGgRU9omXGSDBNzn

Merkle Root

aa7b82facdfbb36d1b7c7d29bf0ce9a67606a5ce2887844235bc18ad27e6343c

Transactions (2)

Coinbasedfdbec189f9a98…392d6378169890

1 in → 53 out10.0300 XPM1.82 KB

AGaKkABV…XGSDBNzn ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5

d10cadf114de0c…bff0e9a607f2be

1 in → 1 out91.8066 XPM192 B

AcUKPiDe…4rznYsnA

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.

1.619 × 10⁹⁹(100-digit number)

16192209308587940888…43659094770812964799

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

1.619 × 10⁹⁹(100-digit number)

16192209308587940888…43659094770812964799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.619 × 10⁹⁹(100-digit number)

16192209308587940888…43659094770812964801

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

3.238 × 10⁹⁹(100-digit number)

32384418617175881776…87318189541625929599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.238 × 10⁹⁹(100-digit number)

32384418617175881776…87318189541625929601

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

6.476 × 10⁹⁹(100-digit number)

64768837234351763553…74636379083251859199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.476 × 10⁹⁹(100-digit number)

64768837234351763553…74636379083251859201

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

1.295 × 10¹⁰⁰(101-digit number)

12953767446870352710…49272758166503718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.295 × 10¹⁰⁰(101-digit number)

12953767446870352710…49272758166503718401

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

2.590 × 10¹⁰⁰(101-digit number)

25907534893740705421…98545516333007436799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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