Block #1,274,748

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/10/2015, 12:18:26 AM · Difficulty 10.8247 · 5,552,443 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bcc54dc332e1de8a0c014a5def0d23714da3ec4595e68d5b158df784f87c3480

View on Chainz ↗

Height

#1,274,748

Difficulty

10.824700

Transactions

Size

1.29 KB

Version

Bits

0ad31f84

Nonce

178,133,835

Timestamp

10/10/2015, 12:18:26 AM

Confirmations

5,552,443

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

dadd429688bea2bd7e021eb635bef49aa5e561a27f86ab3e0f110436899164ed

Transactions (2)

Coinbase2be88f6db8a491…cc0b1cd8624c70

1 in → 1 out8.5400 XPM116 B

AJCEY9yy…tg97E6zm

f1984a8367d192…2912fcd2e63038

7 in → 2 out18.2186 XPM1.08 KB

AHmpcKNo…kfanV9kF AYiipY3n…S2hDxs7e

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.

6.086 × 10⁹⁹(100-digit number)

60865366940091297173…24105235899673477119

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

6.086 × 10⁹⁹(100-digit number)

60865366940091297173…24105235899673477119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.086 × 10⁹⁹(100-digit number)

60865366940091297173…24105235899673477121

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

1.217 × 10¹⁰⁰(101-digit number)

12173073388018259434…48210471799346954239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.217 × 10¹⁰⁰(101-digit number)

12173073388018259434…48210471799346954241

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

2.434 × 10¹⁰⁰(101-digit number)

24346146776036518869…96420943598693908479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.434 × 10¹⁰⁰(101-digit number)

24346146776036518869…96420943598693908481

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

4.869 × 10¹⁰⁰(101-digit number)

48692293552073037738…92841887197387816959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.869 × 10¹⁰⁰(101-digit number)

48692293552073037738…92841887197387816961

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

9.738 × 10¹⁰⁰(101-digit number)

97384587104146075477…85683774394775633919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.738 × 10¹⁰⁰(101-digit number)

97384587104146075477…85683774394775633921

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,274,748

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