Block #1,230,736

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/10/2015, 8:04:03 PM · Difficulty 10.7376 · 5,610,355 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eec3ed8da311fe46b344d9e5605e80727314cf99609ea44b06eed22b476383e9

View on Chainz ↗

Height

#1,230,736

Difficulty

10.737574

Transactions

Size

8.88 KB

Version

Bits

0abcd1ac

Nonce

221,648,540

Timestamp

9/10/2015, 8:04:03 PM

Confirmations

5,610,355

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

1ae60d0a574930a1a802eeca3aa70ed9158748cb35a3a35c67cf0e6ec69fdc53

Transactions (5)

Coinbasef34e03e57422aa…f786b0612b7589

1 in → 1 out8.7800 XPM116 B

AJCEY9yy…tg97E6zm

c862062e89964e…925279e94587e6

52 in → 2 out303.5649 XPM7.58 KB

AYtT99BL…9kUUqdbU AMXMH672…kphfvJ4V

5f8d4e3fc59140…413eaac7f6d079

2 in → 2 out14.8400 XPM374 B

Ac2HGYPt…EHaywxfC ALp5LmLD…BB8fUUPs

4c959b199b7c57…7a6b301d5f4a4c

2 in → 2 out13.6013 XPM375 B

AQa6Cdos…Sk253ama AdUwqsJC…kyCDagPM

c4d6f5ed3a83ae…ceedd6280ff121

2 in → 2 out16.2909 XPM373 B

AMpBMo4v…dM7Z3Jcq ANx3VV9Z…C2wPvF6D

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.

2.771 × 10⁹⁴(95-digit number)

27712551958359854102…45419328967799068379

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

2.771 × 10⁹⁴(95-digit number)

27712551958359854102…45419328967799068379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.771 × 10⁹⁴(95-digit number)

27712551958359854102…45419328967799068381

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

5.542 × 10⁹⁴(95-digit number)

55425103916719708204…90838657935598136759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.542 × 10⁹⁴(95-digit number)

55425103916719708204…90838657935598136761

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

1.108 × 10⁹⁵(96-digit number)

11085020783343941640…81677315871196273519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.108 × 10⁹⁵(96-digit number)

11085020783343941640…81677315871196273521

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

2.217 × 10⁹⁵(96-digit number)

22170041566687883281…63354631742392547039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.217 × 10⁹⁵(96-digit number)

22170041566687883281…63354631742392547041

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

4.434 × 10⁹⁵(96-digit number)

44340083133375766563…26709263484785094079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.434 × 10⁹⁵(96-digit number)

44340083133375766563…26709263484785094081

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 #1,230,736

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