Block #209,983

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 9:13:08 PM · Difficulty 9.9118 · 6,606,975 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a2d0377da3034db1b261511550c394ad7cb8520dd01769c00afd3a41154155ae

View on Chainz ↗

Height

#209,983

Difficulty

9.911820

Transactions

Size

8.66 KB

Version

Bits

09e96d0f

Nonce

100,025

Timestamp

10/14/2013, 9:13:08 PM

Confirmations

6,606,975

Mined by

⛏️ P2SHAaXb6LdzMFohbBjmNyta5dnWNNXefG91jF

Merkle Root

fff99bb5da52bd7ea1ad5956316e21f6d7851cdd3a66c1d74c6a6f00ed4e6c4f

Transactions (4)

Coinbasea8c41940be81f1…09bf71b6e4d9dd

1 in → 1 out10.2700 XPM100 B

AaXb6Ldz…XefG91jF

a27f7878e9cb7e…d86d36f990ea23

72 in → 1 out739.3900 XPM8.06 KB

AUhVxGbt…Az5zVFjy

f3e1464daaf59c…6ad06de2280b5e

1 in → 2 out4.0805 XPM226 B

ANxajfoi…fn3qCY5m ANia7wgK…VR264iFL

34ea500e7c7882…f9dd767bdcdabf

1 in → 1 out2.1390 XPM191 B

AV1Ea59t…YbgD7v2o

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.

7.386 × 10⁹⁷(98-digit number)

73863009403968728156…14259956896469114879

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

7.386 × 10⁹⁷(98-digit number)

73863009403968728156…14259956896469114879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.386 × 10⁹⁷(98-digit number)

73863009403968728156…14259956896469114881

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

1.477 × 10⁹⁸(99-digit number)

14772601880793745631…28519913792938229759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.477 × 10⁹⁸(99-digit number)

14772601880793745631…28519913792938229761

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

2.954 × 10⁹⁸(99-digit number)

29545203761587491262…57039827585876459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.954 × 10⁹⁸(99-digit number)

29545203761587491262…57039827585876459521

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

5.909 × 10⁹⁸(99-digit number)

59090407523174982525…14079655171752919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.909 × 10⁹⁸(99-digit number)

59090407523174982525…14079655171752919041

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

1.181 × 10⁹⁹(100-digit number)

11818081504634996505…28159310343505838079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.181 × 10⁹⁹(100-digit number)

11818081504634996505…28159310343505838081

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

Block #209,983

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