Block #84,515

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 9:24:25 PM · Difficulty 9.2717 · 6,714,851 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f264599e760c1624d24ce85c90bc3fba24c1d111307806ad0edd2ab15ab73833

View on Chainz ↗

Height

#84,515

Difficulty

9.271674

Transactions

Size

724 B

Version

Bits

09458c67

Nonce

4,813

Timestamp

7/26/2013, 9:24:25 PM

Confirmations

6,714,851

Mined by

⛏️ P2SHAcMgz2h5cwY25nNK7GA4fFH2BUjk43HgFS

Merkle Root

981dd8f1512428f6d6603d38beeb351d92c23729a3a853865077a6c3c05d7c8b

Transactions (2)

Coinbaseb9806921865742…d8a2e7d6ef932d

1 in → 1 out11.6300 XPM109 B

AcMgz2h5…jk43HgFS

7e98baeca64803…99ced07c342ced

3 in → 2 out1085.6177 XPM521 B

AS4NDvjA…WVL9Cvd1 AKYH56Gm…gfhbhiAr

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.

1.568 × 10¹⁰³(104-digit number)

15688709255017691836…55999690595501549599

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

1.568 × 10¹⁰³(104-digit number)

15688709255017691836…55999690595501549599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.568 × 10¹⁰³(104-digit number)

15688709255017691836…55999690595501549601

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

3.137 × 10¹⁰³(104-digit number)

31377418510035383672…11999381191003099199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.137 × 10¹⁰³(104-digit number)

31377418510035383672…11999381191003099201

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

6.275 × 10¹⁰³(104-digit number)

62754837020070767345…23998762382006198399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.275 × 10¹⁰³(104-digit number)

62754837020070767345…23998762382006198401

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

1.255 × 10¹⁰⁴(105-digit number)

12550967404014153469…47997524764012396799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.255 × 10¹⁰⁴(105-digit number)

12550967404014153469…47997524764012396801

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

2.510 × 10¹⁰⁴(105-digit number)

25101934808028306938…95995049528024793599

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