Block #208,803

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 5:37:39 AM · Difficulty 9.9073 · 6,583,144 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cbd9257e4dc6173e0e93f96eb8520c8cd89b62eef9c022893b206421fc80020c

View on Chainz ↗

Height

#208,803

Difficulty

9.907293

Transactions

Size

617 B

Version

Bits

09e8445e

Nonce

50,069

Timestamp

10/14/2013, 5:37:39 AM

Confirmations

6,583,144

Merkle Root

b0aa740e239611417ce66b6b67b3c65738cb1719e17b0a710a23482b91386744

Transactions (3)

Coinbasebe876e591a1faf…f84ff2803f2343

1 in → 1 out10.1902 XPM109 B

AX9DLiYr…y4pMsiov

debb4741390a60…c1f3e1d734ab56

1 in → 2 out2268.6514 XPM225 B

AQ66wF4Q…DWcj9p9Y AWjfNchA…3r8YxoQa

94c60e5bb4f2b1…2b55da75c48caa

1 in → 1 out2.9900 XPM192 B

AV5FSQZs…s3jh4xPD

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.

1.021 × 10⁹⁷(98-digit number)

10210498628309153611…33337088699231330559

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

1.021 × 10⁹⁷(98-digit number)

10210498628309153611…33337088699231330559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.021 × 10⁹⁷(98-digit number)

10210498628309153611…33337088699231330561

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

2.042 × 10⁹⁷(98-digit number)

20420997256618307223…66674177398462661119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.042 × 10⁹⁷(98-digit number)

20420997256618307223…66674177398462661121

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

4.084 × 10⁹⁷(98-digit number)

40841994513236614447…33348354796925322239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.084 × 10⁹⁷(98-digit number)

40841994513236614447…33348354796925322241

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

8.168 × 10⁹⁷(98-digit number)

81683989026473228895…66696709593850644479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.168 × 10⁹⁷(98-digit number)

81683989026473228895…66696709593850644481

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

1.633 × 10⁹⁸(99-digit number)

16336797805294645779…33393419187701288959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.633 × 10⁹⁸(99-digit number)

16336797805294645779…33393419187701288961

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