Block #1,233,746

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/12/2015, 7:17:00 PM · Difficulty 10.7469 · 5,583,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

212ab1832e3b41c6b41f0632880db3e9b6bdfd7c7a2847dd924d4fa8049e374b

View on Chainz ↗

Height

#1,233,746

Difficulty

10.746876

Transactions

Size

2.56 KB

Version

Bits

0abf333d

Nonce

80,992

Timestamp

9/12/2015, 7:17:00 PM

Confirmations

5,583,316

Mined by

⛏️ P2SHAHX7m6rTUV4SgWJ3GXnK3mXD4eu5XLVBoC

Merkle Root

25dbf9f247a28a92cc544c2bff5fb20ff6bdb15d7a3b297c0000d074d95f1145

Transactions (5)

Coinbase5da09b409a9268…dde39cf5462851

1 in → 2 out8.6900 XPM145 B

AHX7m6rT…u5XLVBoC Ac7DbgrK…XDMazkvn

39d836f4438600…59f401ed9293a3

10 in → 2 out84.0831 XPM1.52 KB

AGhXVDpi…Yo6Z7LzC AJQQvdkL…rLf5m1ke

00f7fe793aa9f5…56680bb48032b5

2 in → 2 out11.1703 XPM376 B

AbomP3Pg…qkR2w3ur AKNSqmAu…wzaUtqVD

48b5ce04eb4ce2…af38e3153e4715

1 in → 2 out7.1041 XPM226 B

AJSGBngR…KkdHwrDd APHfVo86…ZaZzhZpD

6a4dab16769fe0…1d248bb77db7b1

1 in → 2 out7.6375 XPM227 B

AeRaNNK1…cPN5BiRF AKkWQbtV…5vrGxPNz

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.

1.008 × 10⁹⁹(100-digit number)

10084719934814819380…49290454217653299199

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

1.008 × 10⁹⁹(100-digit number)

10084719934814819380…49290454217653299199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.008 × 10⁹⁹(100-digit number)

10084719934814819380…49290454217653299201

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

2.016 × 10⁹⁹(100-digit number)

20169439869629638761…98580908435306598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.016 × 10⁹⁹(100-digit number)

20169439869629638761…98580908435306598401

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

4.033 × 10⁹⁹(100-digit number)

40338879739259277523…97161816870613196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.033 × 10⁹⁹(100-digit number)

40338879739259277523…97161816870613196801

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

8.067 × 10⁹⁹(100-digit number)

80677759478518555046…94323633741226393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.067 × 10⁹⁹(100-digit number)

80677759478518555046…94323633741226393601

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

1.613 × 10¹⁰⁰(101-digit number)

16135551895703711009…88647267482452787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.613 × 10¹⁰⁰(101-digit number)

16135551895703711009…88647267482452787201

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 #1,233,746

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