Block #1,171,888

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/26/2015, 9:54:08 PM · Difficulty 10.9373 · 5,671,938 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5aae05a692f6d4df99cc5d99d5025bb9e5db1b822e967db0fd579753948184d

View on Chainz ↗

Height

#1,171,888

Difficulty

10.937261

Transactions

Size

2.73 KB

Version

Bits

0aeff054

Nonce

76,946,588

Timestamp

7/26/2015, 9:54:08 PM

Confirmations

5,671,938

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

8c2946531403eda8a093ab2cc7d7c9abfac8c4b987314d41513a1eba34ad4783

Transactions (2)

Coinbase55267ec67a1914…9fced2802617de

1 in → 1 out8.3800 XPM116 B

AJCEY9yy…tg97E6zm

6cb41c8a4cb645…f3ae4053bfc820

17 in → 2 out18.9739 XPM2.53 KB

AVyonWut…ZLEQ5gW1 ANG7zJpm…L37wLboE

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.

3.096 × 10¹⁰⁰(101-digit number)

30964121700955580470…97649747064553471999

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

3.096 × 10¹⁰⁰(101-digit number)

30964121700955580470…97649747064553471999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.096 × 10¹⁰⁰(101-digit number)

30964121700955580470…97649747064553472001

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

6.192 × 10¹⁰⁰(101-digit number)

61928243401911160941…95299494129106943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.192 × 10¹⁰⁰(101-digit number)

61928243401911160941…95299494129106944001

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

1.238 × 10¹⁰¹(102-digit number)

12385648680382232188…90598988258213887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.238 × 10¹⁰¹(102-digit number)

12385648680382232188…90598988258213888001

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

2.477 × 10¹⁰¹(102-digit number)

24771297360764464376…81197976516427775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.477 × 10¹⁰¹(102-digit number)

24771297360764464376…81197976516427776001

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

4.954 × 10¹⁰¹(102-digit number)

49542594721528928752…62395953032855551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.954 × 10¹⁰¹(102-digit number)

49542594721528928752…62395953032855552001

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

9.908 × 10¹⁰¹(102-digit number)

99085189443057857505…24791906065711103999

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

Block #1,171,888

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