Block #303,713

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/10/2013, 12:55:40 PM · Difficulty 9.9931 · 6,501,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

39589eef259645640bb4ee47aed85ef7228fb0758a97fdf07b32bf71e276e1d5

View on Chainz ↗

Height

#303,713

Difficulty

9.993101

Transactions

Size

2.10 KB

Version

Bits

09fe3be0

Nonce

39,151

Timestamp

12/10/2013, 12:55:40 PM

Confirmations

6,501,191

Mined by

⛏️ aaRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

28900acb66f293d88e466e43ba2a0a4a5bcb4933179859eb6b8a41e6093a6748

Transactions (4)

Coinbase8dcf21ad9beccd…5faeeccf2fd36a

1 in → 30 out9.9800 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AZ2pPuKg…95SN2Yr7 AQf7sjuh…sNY5fXpu ARcqMJhp…RVLToQ6S APeshfYV…3PKcKMKH

cb8f4c601c9df5…5f340010873776

3 in → 2 out10.0246 XPM523 B

AGDVFHDW…ZEDnR5Uk AePc3qoS…8LAjC5dg

0a0c2db68a9d7d…b20fccbad8e4e5

1 in → 2 out6.6422 XPM226 B

AHiqzUT7…gZ2zy4Dq AHb9jgCd…tL7Th5xX

7ca784df7592e2…4bb5c277db9101

1 in → 2 out5.6415 XPM225 B

AaN24Sdd…Hcpi2k9g AdyEcm7D…ymqUw7a7

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.

7.015 × 10⁹⁶(97-digit number)

70158831030649924622…19727423847067496319

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

7.015 × 10⁹⁶(97-digit number)

70158831030649924622…19727423847067496319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.015 × 10⁹⁶(97-digit number)

70158831030649924622…19727423847067496321

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

1.403 × 10⁹⁷(98-digit number)

14031766206129984924…39454847694134992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.403 × 10⁹⁷(98-digit number)

14031766206129984924…39454847694134992641

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

2.806 × 10⁹⁷(98-digit number)

28063532412259969848…78909695388269985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.806 × 10⁹⁷(98-digit number)

28063532412259969848…78909695388269985281

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

5.612 × 10⁹⁷(98-digit number)

56127064824519939697…57819390776539970559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.612 × 10⁹⁷(98-digit number)

56127064824519939697…57819390776539970561

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

1.122 × 10⁹⁸(99-digit number)

11225412964903987939…15638781553079941119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.122 × 10⁹⁸(99-digit number)

11225412964903987939…15638781553079941121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.245 × 10⁹⁸(99-digit number)

22450825929807975879…31277563106159882239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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