Block #1,428,651

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2016, 8:18:25 AM · Difficulty 10.7425 · 5,413,594 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5033f62866eed0bb4d8dee8ca4c15ae3f9038e6cf8819625792aaf50546f292c

View on Chainz ↗

Height

#1,428,651

Difficulty

10.742535

Transactions

Size

8.01 KB

Version

Bits

0abe16c7

Nonce

491,645,544

Timestamp

1/26/2016, 8:18:25 AM

Confirmations

5,413,594

Mined by

⛏️ P2SHASRJyFMVy5R2p7jHXmUjowZzAB2mEDspXe

Merkle Root

0b2c42784718ce677a4c578e577ab9f646fa170c4f6cbb620f4895a274352f10

Transactions (3)

Coinbasedf13c1d8f0c283…21e7196d817f49

1 in → 1 out8.7500 XPM110 B

ASRJyFMV…2mEDspXe

0f9eed1d315193…d35cbed3652c7e

1 in → 2 out57541.6915 XPM226 B

AL9LcrjH…MSYbdLUv AHNkwmbJ…EUxEmniY

70f079fc72418c…600e8870156b99

52 in → 2 out1007.5400 XPM7.59 KB

AcDhjHA9…ebukETHz AdunoF3o…UYbJWZVb

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.

6.842 × 10⁹³(94-digit number)

68421969395697958551…92212836542359511999

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

6.842 × 10⁹³(94-digit number)

68421969395697958551…92212836542359511999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.842 × 10⁹³(94-digit number)

68421969395697958551…92212836542359512001

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

1.368 × 10⁹⁴(95-digit number)

13684393879139591710…84425673084719023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.368 × 10⁹⁴(95-digit number)

13684393879139591710…84425673084719024001

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

2.736 × 10⁹⁴(95-digit number)

27368787758279183420…68851346169438047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.736 × 10⁹⁴(95-digit number)

27368787758279183420…68851346169438048001

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

5.473 × 10⁹⁴(95-digit number)

54737575516558366840…37702692338876095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.473 × 10⁹⁴(95-digit number)

54737575516558366840…37702692338876096001

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

1.094 × 10⁹⁵(96-digit number)

10947515103311673368…75405384677752191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.094 × 10⁹⁵(96-digit number)

10947515103311673368…75405384677752192001

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 #1,428,651

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