Block #86,450

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 3:34:39 AM · Difficulty 9.2901 · 6,708,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3d30cfc35d7c4349deedfbee707e4724beabaa35404511981b49c1df25f82f1

View on Chainz ↗

Height

#86,450

Difficulty

9.290120

Transactions

Size

12.73 KB

Version

Bits

094a4547

Nonce

126,862

Timestamp

7/28/2013, 3:34:39 AM

Confirmations

6,708,131

Mined by

⛏️ P2SHASjsJAq4tMTLVFfRC5iW86oKcE1JTtsUr1

Merkle Root

7283995023dbe583f25d870f97f050b26d7e41774124b08b87b1b903073f7923

Transactions (4)

Coinbase31aa66a3ab322c…90dea2d8c5d6c3

1 in → 1 out11.7100 XPM109 B

ASjsJAq4…1JTtsUr1

fa902102484253…f7bb5b271fa22b

102 in → 2 out1174.8200 XPM11.46 KB

ALqKt6TX…mDLeyVea AGfz3APU…kNJNtgfb

b37397a9afdc85…393fb3e64b8bb8

5 in → 2 out51.4461 XPM817 B

AWidNrYb…oUuJQeoU Achmusid…dSSMpK8W

e29353c215a8a4…e0b863da37be63

2 in → 1 out23.2100 XPM271 B

APJQPoT9…6ivDKPnG

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.

9.442 × 10¹¹⁰(111-digit number)

94429524124193264694…52679474589349631599

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

9.442 × 10¹¹⁰(111-digit number)

94429524124193264694…52679474589349631599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.442 × 10¹¹⁰(111-digit number)

94429524124193264694…52679474589349631601

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

1.888 × 10¹¹¹(112-digit number)

18885904824838652938…05358949178699263199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.888 × 10¹¹¹(112-digit number)

18885904824838652938…05358949178699263201

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

3.777 × 10¹¹¹(112-digit number)

37771809649677305877…10717898357398526399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.777 × 10¹¹¹(112-digit number)

37771809649677305877…10717898357398526401

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

7.554 × 10¹¹¹(112-digit number)

75543619299354611755…21435796714797052799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.554 × 10¹¹¹(112-digit number)

75543619299354611755…21435796714797052801

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

1.510 × 10¹¹²(113-digit number)

15108723859870922351…42871593429594105599

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