Block #198,868

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 12:19:59 AM · Difficulty 9.8867 · 6,607,199 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a258f5859b54b513e78c01f100aa590640b3fc352a076b8b4fd35acca58c8fdb

View on Chainz ↗

Height

#198,868

Difficulty

9.886734

Transactions

Size

1.08 KB

Version

Bits

09e30106

Nonce

110,803

Timestamp

10/8/2013, 12:19:59 AM

Confirmations

6,607,199

Mined by

⛏️ P2SHAct9nbnxouu2cJ2guUKhQ1aK94p3qMGBEU

Merkle Root

82d128c60ee2abe449d95c451afecc8e2d8e31936f4be25ee6450302c11f4475

Transactions (4)

Coinbasead9a99f96fe720…5aab21479ac038

1 in → 1 out10.2500 XPM109 B

Act9nbnx…p3qMGBEU

cdd07d102e1a20…0e2139b447256e

2 in → 2 out20.5100 XPM308 B

AbjxLoGE…FXwrp5Ju ARzZ8TPx…Q9tbJWWk

a9e0edc525db71…c1e4d0482d55bd

2 in → 2 out13.3766 XPM375 B

AeJpEDyZ…fh38vV2Y AZBifnBc…sJXZqSaw

f14770a5798b8f…0c3853d43a4d54

1 in → 2 out3.3444 XPM226 B

AG415EMc…Vc68Rvji AcVUgB6x…y6Rmm2sv

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.

1.249 × 10⁹⁵(96-digit number)

12497207912269976844…45946320777093016319

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

1.249 × 10⁹⁵(96-digit number)

12497207912269976844…45946320777093016319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.249 × 10⁹⁵(96-digit number)

12497207912269976844…45946320777093016321

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

2.499 × 10⁹⁵(96-digit number)

24994415824539953688…91892641554186032639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.499 × 10⁹⁵(96-digit number)

24994415824539953688…91892641554186032641

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

4.998 × 10⁹⁵(96-digit number)

49988831649079907377…83785283108372065279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.998 × 10⁹⁵(96-digit number)

49988831649079907377…83785283108372065281

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

9.997 × 10⁹⁵(96-digit number)

99977663298159814754…67570566216744130559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.997 × 10⁹⁵(96-digit number)

99977663298159814754…67570566216744130561

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

1.999 × 10⁹⁶(97-digit number)

19995532659631962950…35141132433488261119

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