Block #85,614

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 1:25:32 PM · Difficulty 9.2916 · 6,711,198 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44d0e683e4f80cfd30151aa3a24905e705cd926dd29448891634592e68336cc9

View on Chainz ↗

Height

#85,614

Difficulty

9.291642

Transactions

Size

585 B

Version

Bits

094aa90f

Nonce

73,088

Timestamp

7/27/2013, 1:25:32 PM

Confirmations

6,711,198

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

f04a47ea0aa13b7952c353b0c68f9bcf7cdbee5b70dffbcc25b19ed81d86840b

Transactions (3)

Coinbasef3e6fe24a34dad…39d04e684995b7

1 in → 1 out11.5900 XPM109 B

AcuJraLT…Y66BS47Q

c1d9ba4f576ea3…4c9700731901ce

1 in → 1 out11.6100 XPM157 B

AdHH4S7H…YBpU1DpD

e0ccff3d536968…d524678407a42d

1 in → 2 out3.5015 XPM227 B

AUKHL3eL…skSF7HRM AcemkB4r…wUs8AxQo

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.

1.849 × 10⁹⁸(99-digit number)

18492021882296948433…23962019637312145759

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

1.849 × 10⁹⁸(99-digit number)

18492021882296948433…23962019637312145759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.849 × 10⁹⁸(99-digit number)

18492021882296948433…23962019637312145761

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

3.698 × 10⁹⁸(99-digit number)

36984043764593896866…47924039274624291519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.698 × 10⁹⁸(99-digit number)

36984043764593896866…47924039274624291521

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

7.396 × 10⁹⁸(99-digit number)

73968087529187793733…95848078549248583039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.396 × 10⁹⁸(99-digit number)

73968087529187793733…95848078549248583041

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

1.479 × 10⁹⁹(100-digit number)

14793617505837558746…91696157098497166079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.479 × 10⁹⁹(100-digit number)

14793617505837558746…91696157098497166081

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

2.958 × 10⁹⁹(100-digit number)

29587235011675117493…83392314196994332159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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