Block #89,704

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 1:52:46 PM · Difficulty 9.2547 · 6,704,629 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72c27f8f723bd85448cd18b164a7078f4063f939514ac39230c7f16135f0f701

View on Chainz ↗

Height

#89,704

Difficulty

9.254678

Transactions

Size

2.45 KB

Version

Bits

09413298

Nonce

25,741

Timestamp

7/30/2013, 1:52:46 PM

Confirmations

6,704,629

Merkle Root

00e4aae30446154d8871d9d51af2609e47a18cb233c3c78deeaeaceb4894ee16

Transactions (5)

Coinbase35a6a8bfdd1798…f802324ae723a6

1 in → 1 out11.7000 XPM109 B

ARFuywxY…SeUaa6Zq

cafa02142ff5ee…56c039fd76101d

3 in → 4 out8.3964 XPM589 B

AMdf2JPw…URZXPvPS AYMpcVoL…q4uwzeTU AbABiPuR…YD1F57r5 AckP6nZ5…hBzFsNFH

20529dd2ad33c4…c917c450122d6a

4 in → 2 out5.2580 XPM672 B

AR1r95b3…tnovbWrt AQYHqSET…8dCXSYue

b177d5a0462fd1…797c81b9765f7c

3 in → 2 out1.1028 XPM523 B

AKEnMiea…6sxNVJCJ AQYHqSET…8dCXSYue

00beacdf6d7acb…a947151ade78ba

3 in → 2 out3.7045 XPM523 B

AQYHqSET…8dCXSYue ALzYbqSb…ZmJEDJyb

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.

3.599 × 10¹⁰⁸(109-digit number)

35994548757427630234…27478902783016054159

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

3.599 × 10¹⁰⁸(109-digit number)

35994548757427630234…27478902783016054159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.599 × 10¹⁰⁸(109-digit number)

35994548757427630234…27478902783016054161

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

7.198 × 10¹⁰⁸(109-digit number)

71989097514855260469…54957805566032108319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.198 × 10¹⁰⁸(109-digit number)

71989097514855260469…54957805566032108321

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

1.439 × 10¹⁰⁹(110-digit number)

14397819502971052093…09915611132064216639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.439 × 10¹⁰⁹(110-digit number)

14397819502971052093…09915611132064216641

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

2.879 × 10¹⁰⁹(110-digit number)

28795639005942104187…19831222264128433279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.879 × 10¹⁰⁹(110-digit number)

28795639005942104187…19831222264128433281

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

5.759 × 10¹⁰⁹(110-digit number)

57591278011884208375…39662444528256866559

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