Block #1,234,497

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/13/2015, 7:22:29 AM · Difficulty 10.7480 · 5,561,763 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

791802f9ef6a1a3ae5ea600ddde4535a777f2e0cdf0f4049513a20aed4f9c8ea

View on Chainz ↗

Height

#1,234,497

Difficulty

10.748029

Transactions

Size

956 B

Version

Bits

0abf7ecf

Nonce

1,208,435,592

Timestamp

9/13/2015, 7:22:29 AM

Confirmations

5,561,763

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

651893d6cb36eeb896833e4c26d61188a31abc9498606b3f425e97497b7dfd23

Transactions (3)

Coinbase4b61fc84bd4916…a183c5d5c1ae01

1 in → 1 out8.6600 XPM116 B

AJCEY9yy…tg97E6zm

4b92119fc22150…80eb8d97d984d1

2 in → 2 out17.3200 XPM373 B

AaqRBcTJ…x4yCUsHi AJRwGPSP…QDRWdi2B

34ec2ff3f5a6d5…b7f2d9f7293593

2 in → 2 out12.4152 XPM376 B

AFxSJbfW…jNJBBcKQ ANeMre2C…MFDCgCnr

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.

1.278 × 10⁹⁸(99-digit number)

12785357882767052582…07736099107235430399

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

1.278 × 10⁹⁸(99-digit number)

12785357882767052582…07736099107235430399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.278 × 10⁹⁸(99-digit number)

12785357882767052582…07736099107235430401

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

2.557 × 10⁹⁸(99-digit number)

25570715765534105165…15472198214470860799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.557 × 10⁹⁸(99-digit number)

25570715765534105165…15472198214470860801

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

5.114 × 10⁹⁸(99-digit number)

51141431531068210330…30944396428941721599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.114 × 10⁹⁸(99-digit number)

51141431531068210330…30944396428941721601

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

1.022 × 10⁹⁹(100-digit number)

10228286306213642066…61888792857883443199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.022 × 10⁹⁹(100-digit number)

10228286306213642066…61888792857883443201

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

2.045 × 10⁹⁹(100-digit number)

20456572612427284132…23777585715766886399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.045 × 10⁹⁹(100-digit number)

20456572612427284132…23777585715766886401

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