Block #189,752

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 12:33:12 AM · Difficulty 9.8738 · 6,619,956 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9386457d8b618bfe9a2d482e6139c4bd0af815b61d151410b1508b6882c88fd

View on Chainz ↗

Height

#189,752

Difficulty

9.873793

Transactions

Size

3.07 KB

Version

Bits

09dfb0ec

Nonce

1,164,836,308

Timestamp

10/2/2013, 12:33:12 AM

Confirmations

6,619,956

Mined by

⛏️ 8RKiAebfwVBz4JXqpPSQCTmJaqhKfFZtQwaXb8

Merkle Root

1677cf2c6df0e2da050df51f7db9380d412c5d17819666766d518ce2f1c23798

Transactions (1)

Coinbase1677cf2c6df0e2…518ce2f1c23798

1 in → 88 out10.2100 XPM2.98 KB

AebfwVBz…ZtQwaXb8 ANBtDhv7…saWQoBRP APuVQWHc…wmkgqriM AXX6qV1p…P5nUERYS AWNQupAN…aZuvsT36

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.

4.942 × 10⁹⁷(98-digit number)

49424423693172238994…03604772524047359999

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

4.942 × 10⁹⁷(98-digit number)

49424423693172238994…03604772524047359999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.942 × 10⁹⁷(98-digit number)

49424423693172238994…03604772524047360001

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

9.884 × 10⁹⁷(98-digit number)

98848847386344477989…07209545048094719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.884 × 10⁹⁷(98-digit number)

98848847386344477989…07209545048094720001

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

1.976 × 10⁹⁸(99-digit number)

19769769477268895597…14419090096189439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.976 × 10⁹⁸(99-digit number)

19769769477268895597…14419090096189440001

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

3.953 × 10⁹⁸(99-digit number)

39539538954537791195…28838180192378879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.953 × 10⁹⁸(99-digit number)

39539538954537791195…28838180192378880001

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

7.907 × 10⁹⁸(99-digit number)

79079077909075582391…57676360384757759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.907 × 10⁹⁸(99-digit number)

79079077909075582391…57676360384757760001

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 #189,752

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