Block #2,054,134

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2017, 8:44:58 AM · Difficulty 10.7876 · 4,773,102 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

47ccf36eafd045cae2e5c3a79265890312d8d347a3601323de13e6382a35f32d

View on Chainz ↗

Height

#2,054,134

Difficulty

10.787611

Transactions

Size

1017 B

Version

Bits

0ac9a0e1

Nonce

242,102,046

Timestamp

4/4/2017, 8:44:58 AM

Confirmations

4,773,102

Mined by

⛏️ P2SHAUvR8WKnSMXa7TTyomb93CQcfsQ9m2cCLW

Merkle Root

a4820a19dfdaddc3368f318d9c8979d9b04e6d837603adccfd05a393772b7679

Transactions (2)

Coinbaseceb1ab59f7c9ee…9859d6f3868e8e

1 in → 1 out8.5900 XPM109 B

AUvR8WKn…Q9m2cCLW

5356243c961cd9…16e36a004b2f43

5 in → 2 out3304.6300 XPM817 B

AdWsowVT…Vhj9XiTv AKF5aWAG…627Qwi4s

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.

8.477 × 10⁹⁷(98-digit number)

84771856021394126006…61301526011324334079

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

8.477 × 10⁹⁷(98-digit number)

84771856021394126006…61301526011324334079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.477 × 10⁹⁷(98-digit number)

84771856021394126006…61301526011324334081

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

1.695 × 10⁹⁸(99-digit number)

16954371204278825201…22603052022648668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.695 × 10⁹⁸(99-digit number)

16954371204278825201…22603052022648668161

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

3.390 × 10⁹⁸(99-digit number)

33908742408557650402…45206104045297336319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.390 × 10⁹⁸(99-digit number)

33908742408557650402…45206104045297336321

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

6.781 × 10⁹⁸(99-digit number)

67817484817115300805…90412208090594672639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.781 × 10⁹⁸(99-digit number)

67817484817115300805…90412208090594672641

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

1.356 × 10⁹⁹(100-digit number)

13563496963423060161…80824416181189345279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.356 × 10⁹⁹(100-digit number)

13563496963423060161…80824416181189345281

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 #2,054,134

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