Block #1,221,268

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/4/2015, 5:35:37 AM · Difficulty 10.7395 · 5,571,378 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65c4bede02d694e89d58cc9d580f2df6d64efd4063986b92f3ede0a0025c2c9c

View on Chainz ↗

Height

#1,221,268

Difficulty

10.739504

Transactions

Size

2.38 KB

Version

Bits

0abd501d

Nonce

172,444,797

Timestamp

9/4/2015, 5:35:37 AM

Confirmations

5,571,378

Merkle Root

df678e2196cb4c6fcdf1c4438c2e794bce86964d64a7dcadaf5f00d647354d11

Transactions (5)

Coinbase0bc9f52c6a7fb6…ca124fa76d68ea

1 in → 1 out8.7100 XPM110 B

AcPVjibG…DDwwSXsk

5e4e4913862e0a…61b0fd4bb5d024

1 in → 2 out8.6100 XPM225 B

AZp84AN3…xwi9EEnC AYePcm2q…Lhs5UmMm

3a73822181ad77…ffd4c4d0632a81

9 in → 2 out80.9264 XPM1.38 KB

AetrfQ87…woiwY748 AdLaTuGz…oyZ2dDtu

2cdc326369c0da…b7dfad1de45553

2 in → 2 out10.0190 XPM376 B

AJrzf33Q…cB4zqUUs AJRwGPSP…QDRWdi2B

b238a98e0a53dc…c88570063e5c31

1 in → 2 out6.5356 XPM227 B

Aa4PtTwK…H3ppZFzk AT1mHWfJ…BxDEuxdf

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.

1.536 × 10⁹⁷(98-digit number)

15362115791035443021…04007021703768965119

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

1.536 × 10⁹⁷(98-digit number)

15362115791035443021…04007021703768965119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.536 × 10⁹⁷(98-digit number)

15362115791035443021…04007021703768965121

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

3.072 × 10⁹⁷(98-digit number)

30724231582070886043…08014043407537930239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.072 × 10⁹⁷(98-digit number)

30724231582070886043…08014043407537930241

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

6.144 × 10⁹⁷(98-digit number)

61448463164141772087…16028086815075860479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.144 × 10⁹⁷(98-digit number)

61448463164141772087…16028086815075860481

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

1.228 × 10⁹⁸(99-digit number)

12289692632828354417…32056173630151720959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.228 × 10⁹⁸(99-digit number)

12289692632828354417…32056173630151720961

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

2.457 × 10⁹⁸(99-digit number)

24579385265656708834…64112347260303441919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.457 × 10⁹⁸(99-digit number)

24579385265656708834…64112347260303441921

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