Block #88,397

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 2:41:31 PM · Difficulty 9.2672 · 6,715,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81449545fa3c337d737d1f366a173595884ac9aa32eab06f4360b3fd4fa98195

View on Chainz ↗

Height

#88,397

Difficulty

9.267159

Transactions

Size

2.04 KB

Version

Bits

0944648c

Nonce

143,954

Timestamp

7/29/2013, 2:41:31 PM

Confirmations

6,715,366

Mined by

⛏️ P2SHAVBUEab8dBMeCsnvFuLLHR4aFkhr1tszUE

Merkle Root

c41105661cfd99beb4b4ea0ffe2037a1b7d1722b54cd0ceb7fef8615881fe5d8

Transactions (5)

Coinbase5e7f2d3ff45ad0…0003748c669dde

1 in → 1 out11.6700 XPM109 B

AVBUEab8…hr1tszUE

b7bfbea932604b…96fa0a650c5b60

3 in → 2 out9462.4940 XPM521 B

AGWg2Wog…f7y6cCuZ AWSv6hg4…QvGk9TGY

fe560863c7f225…f8566cbec4de47

4 in → 1 out137.3437 XPM570 B

AQKwR1Zd…md5GhQYC

9863c6877afd85…896d9f99a3b011

3 in → 2 out600.0137 XPM522 B

AWFXdK9J…nsDvoB1R AVHDMzPN…YkDugNUk

637963150231f3…ecf7839474cf28

2 in → 1 out23.3200 XPM271 B

AdJbSNCM…VdXUWZw8

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.

6.643 × 10¹¹⁰(111-digit number)

66434919878348438319…19947510573325011649

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

6.643 × 10¹¹⁰(111-digit number)

66434919878348438319…19947510573325011649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.643 × 10¹¹⁰(111-digit number)

66434919878348438319…19947510573325011651

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

1.328 × 10¹¹¹(112-digit number)

13286983975669687663…39895021146650023299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.328 × 10¹¹¹(112-digit number)

13286983975669687663…39895021146650023301

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

2.657 × 10¹¹¹(112-digit number)

26573967951339375327…79790042293300046599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.657 × 10¹¹¹(112-digit number)

26573967951339375327…79790042293300046601

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

5.314 × 10¹¹¹(112-digit number)

53147935902678750655…59580084586600093199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.314 × 10¹¹¹(112-digit number)

53147935902678750655…59580084586600093201

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

1.062 × 10¹¹²(113-digit number)

10629587180535750131…19160169173200186399

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