Block #357,175

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/13/2014, 6:03:16 AM · Difficulty 10.3821 · 6,436,091 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aed5950cdb6bbb83bebc6f84d3b80498f56bb3dcdc969eb18fb845e70ff49be1

View on Chainz ↗

Height

#357,175

Difficulty

10.382074

Transactions

Size

10.51 KB

Version

Bits

0a61cf95

Nonce

338,291

Timestamp

1/13/2014, 6:03:16 AM

Confirmations

6,436,091

Merkle Root

ddc16c5be43ec484b7f770626232e0dd9d59276991649f2d981669567a85a386

Transactions (4)

Coinbaseca42de1e7637f3…505e7759f14786

1 in → 1 out9.3800 XPM110 B

AeKNrjNj…1NEq95Ta

99e45d27462cce…f0f19410afc9dd

3 in → 2 out83.7001 XPM523 B

AeWK6Zk2…L5BsDAtZ AQabgqPC…BR75E7v3

3256ebd61dbf83…327b3b676a9ed3

1 in → 1 out3.0017 XPM191 B

AQ7CPjhw…fxeUh3L8

41c21e3f12c418…26895fcf82bff8

66 in → 2 out21.8146 XPM9.61 KB

APGVU8e4…VvHzSKoJ AdKEgJo4…p6sjthXW

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.

1.524 × 10⁹⁹(100-digit number)

15242235601428546733…80610176115685708519

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

1.524 × 10⁹⁹(100-digit number)

15242235601428546733…80610176115685708519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.524 × 10⁹⁹(100-digit number)

15242235601428546733…80610176115685708521

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

3.048 × 10⁹⁹(100-digit number)

30484471202857093467…61220352231371417039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.048 × 10⁹⁹(100-digit number)

30484471202857093467…61220352231371417041

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

6.096 × 10⁹⁹(100-digit number)

60968942405714186934…22440704462742834079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.096 × 10⁹⁹(100-digit number)

60968942405714186934…22440704462742834081

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

1.219 × 10¹⁰⁰(101-digit number)

12193788481142837386…44881408925485668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.219 × 10¹⁰⁰(101-digit number)

12193788481142837386…44881408925485668161

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

2.438 × 10¹⁰⁰(101-digit number)

24387576962285674773…89762817850971336319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.438 × 10¹⁰⁰(101-digit number)

24387576962285674773…89762817850971336321

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

4.877 × 10¹⁰⁰(101-digit number)

48775153924571349547…79525635701942672639

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