Block #289,210

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 2:36:22 AM · Difficulty 9.9883 · 6,521,863 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

38771966a8a227a668a6abdb2af2e71951be9387b680195e35629ba9d6e14ae0

View on Chainz ↗

Height

#289,210

Difficulty

9.988344

Transactions

Size

1.05 KB

Version

Bits

09fd0420

Nonce

103,962

Timestamp

12/2/2013, 2:36:22 AM

Confirmations

6,521,863

Mined by

⛏️ iaRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

072914aa88c52195b4114b8a2154dc40b1db8b26a8f207bca299446119b904fc

Transactions (1)

Coinbase072914aa88c521…99446119b904fc

1 in → 27 out10.0100 XPM981 B

AYcLTeXR…bscgPops Ad9pSzHt…cpJ3y2zz ALSiuDiS…WqQxGQSY AGFAJ5YL…ZEnBbk6G AN63YyQR…1tfe566A

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.

2.930 × 10⁹⁵(96-digit number)

29308687041179252933…88432446512388850879

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

2.930 × 10⁹⁵(96-digit number)

29308687041179252933…88432446512388850879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.930 × 10⁹⁵(96-digit number)

29308687041179252933…88432446512388850881

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

5.861 × 10⁹⁵(96-digit number)

58617374082358505867…76864893024777701759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.861 × 10⁹⁵(96-digit number)

58617374082358505867…76864893024777701761

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

1.172 × 10⁹⁶(97-digit number)

11723474816471701173…53729786049555403519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.172 × 10⁹⁶(97-digit number)

11723474816471701173…53729786049555403521

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

2.344 × 10⁹⁶(97-digit number)

23446949632943402346…07459572099110807039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.344 × 10⁹⁶(97-digit number)

23446949632943402346…07459572099110807041

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

4.689 × 10⁹⁶(97-digit number)

46893899265886804693…14919144198221614079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.689 × 10⁹⁶(97-digit number)

46893899265886804693…14919144198221614081

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 #289,210

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