Block #1,407,645

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2016, 6:42:06 PM · Difficulty 10.8047 · 5,418,869 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

492841261314a6a86cb53030c2b7e42f3638fd51c4d320e8390eff44c25529d6

View on Chainz ↗

Height

#1,407,645

Difficulty

10.804743

Transactions

Size

1.36 KB

Version

Bits

0ace03ab

Nonce

1,098,806,795

Timestamp

1/10/2016, 6:42:06 PM

Confirmations

5,418,869

Mined by

⛏️ P2SHAN4x2qUdPUZGUEoY32M8XTYAK1rGdiNVwp

Merkle Root

eb9c45f37eaa10d8ef3782945f9d0510a66b7632bb55cafae6600b7cd3d55904

Transactions (3)

Coinbasefb595702b2c129…d829bf44b1bb4c

1 in → 1 out8.5700 XPM110 B

AN4x2qUd…rGdiNVwp

f136c4b9b118d8…837803cc87ee3b

4 in → 2 out1.7349 XPM669 B

AQKTBsct…XRHnu34m ASXTjNyM…RS6P8LH3

a0c902181919b2…f57dab623cac3c

3 in → 2 out0.4463 XPM522 B

ARSNuKDX…FGSD7ZP7 AMQLEnhP…5ZVjiLr2

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.

1.275 × 10⁹⁷(98-digit number)

12759591019680177825…83305737185784750079

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

1.275 × 10⁹⁷(98-digit number)

12759591019680177825…83305737185784750079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.275 × 10⁹⁷(98-digit number)

12759591019680177825…83305737185784750081

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

2.551 × 10⁹⁷(98-digit number)

25519182039360355650…66611474371569500159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.551 × 10⁹⁷(98-digit number)

25519182039360355650…66611474371569500161

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

5.103 × 10⁹⁷(98-digit number)

51038364078720711300…33222948743139000319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.103 × 10⁹⁷(98-digit number)

51038364078720711300…33222948743139000321

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

1.020 × 10⁹⁸(99-digit number)

10207672815744142260…66445897486278000639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10⁹⁸(99-digit number)

10207672815744142260…66445897486278000641

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

2.041 × 10⁹⁸(99-digit number)

20415345631488284520…32891794972556001279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.041 × 10⁹⁸(99-digit number)

20415345631488284520…32891794972556001281

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 #1,407,645

Cookie Preferences