Block #1,424,684

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2016, 3:07:27 AM · Difficulty 10.7742 · 5,418,143 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d40ae52481f6f0f33b65e6e892129f672d1a366e61e5a4060e0584b500145bf

View on Chainz ↗

Height

#1,424,684

Difficulty

10.774181

Transactions

Size

730 B

Version

Bits

0ac630b4

Nonce

1,685,460,256

Timestamp

1/23/2016, 3:07:27 AM

Confirmations

5,418,143

Mined by

⛏️ P2SHAbUyi2vGFKAitbJY28EiThGvL9VGd4pYPB

Merkle Root

87c6d07812982a9ef054c8667bb0bab2d9fdf9939ee53576ac5dffa189b0cb0c

Transactions (2)

Coinbase6fd6c3e0ace9a7…ad375440802229

1 in → 1 out8.6100 XPM109 B

AbUyi2vG…VGd4pYPB

774ab5528d73dc…823a6ca9899043

1 in → 11 out265.4059 XPM531 B

AXB2iJzr…VapWHkrP AW6zRY4z…ELnj21DS AJXcikW2…tmvDZmPB AJdFVNXw…pyeMC1s9 AMj7L3Ao…HMF1Fq3W

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.

9.031 × 10⁹⁵(96-digit number)

90316133017950886505…64739260767213384959

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

9.031 × 10⁹⁵(96-digit number)

90316133017950886505…64739260767213384959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.031 × 10⁹⁵(96-digit number)

90316133017950886505…64739260767213384961

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

1.806 × 10⁹⁶(97-digit number)

18063226603590177301…29478521534426769919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.806 × 10⁹⁶(97-digit number)

18063226603590177301…29478521534426769921

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

3.612 × 10⁹⁶(97-digit number)

36126453207180354602…58957043068853539839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.612 × 10⁹⁶(97-digit number)

36126453207180354602…58957043068853539841

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

7.225 × 10⁹⁶(97-digit number)

72252906414360709204…17914086137707079679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.225 × 10⁹⁶(97-digit number)

72252906414360709204…17914086137707079681

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

1.445 × 10⁹⁷(98-digit number)

14450581282872141840…35828172275414159359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.445 × 10⁹⁷(98-digit number)

14450581282872141840…35828172275414159361

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 #1,424,684

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