Block #1,359,404

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2015, 2:06:13 PM · Difficulty 10.8382 · 5,448,728 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0c6718c30b3247f01200dca483134dea1c5f87d7a43a4b54362a8935e7487e8

View on Chainz ↗

Height

#1,359,404

Difficulty

10.838188

Transactions

Size

2.32 KB

Version

Bits

0ad69378

Nonce

322,952,026

Timestamp

12/7/2015, 2:06:13 PM

Confirmations

5,448,728

Mined by

⛏️ P2SHASnJ26W5E8W3TgdC3paCxJeY2rYMWymHNr

Merkle Root

31c2d2a35dd3444a541821a97aaea9981263bb5629c1bfa2c31b9db2a48d64dd

Transactions (4)

Coinbaseaedd5e9a55c785…24f1d3fd55aad9

1 in → 1 out8.5400 XPM110 B

ASnJ26W5…YMWymHNr

d25ddf792934a5…e007a41cfc52a9

7 in → 2 out2897.3782 XPM1.09 KB

Ae3nhxzM…4KBH3euP AHccrvox…rZxQitpx

ec0b1b714a6cd6…e971cac3cd1551

1 in → 1 out8.4545 XPM157 B

AeUgpiui…YCFJEgYU

10a93ce0cbabdb…1e369a839acbe2

1 in → 22 out1.1270 XPM905 B

AQBM6QwX…ZrPhSx4C AMjum32j…okZzjP2A AQppDAHZ…HzsaE5ca AGGC96kT…tgntK4X9 AXn94E9d…xKzG1Yrs

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.

3.693 × 10⁹⁴(95-digit number)

36937581004025042071…18734071018470691199

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

3.693 × 10⁹⁴(95-digit number)

36937581004025042071…18734071018470691199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.693 × 10⁹⁴(95-digit number)

36937581004025042071…18734071018470691201

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

7.387 × 10⁹⁴(95-digit number)

73875162008050084143…37468142036941382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.387 × 10⁹⁴(95-digit number)

73875162008050084143…37468142036941382401

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

1.477 × 10⁹⁵(96-digit number)

14775032401610016828…74936284073882764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.477 × 10⁹⁵(96-digit number)

14775032401610016828…74936284073882764801

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

2.955 × 10⁹⁵(96-digit number)

29550064803220033657…49872568147765529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.955 × 10⁹⁵(96-digit number)

29550064803220033657…49872568147765529601

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

5.910 × 10⁹⁵(96-digit number)

59100129606440067314…99745136295531059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.910 × 10⁹⁵(96-digit number)

59100129606440067314…99745136295531059201

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 #1,359,404

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