Block #1,453,406

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/12/2016, 6:06:54 PM · Difficulty 10.7272 · 5,386,376 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

424da66355487cabbd68f63cbfd6caef76550fd45e180365322719358e643d57

View on Chainz ↗

Height

#1,453,406

Difficulty

10.727176

Transactions

Size

31.79 KB

Version

Bits

0aba2830

Nonce

324,466,770

Timestamp

2/12/2016, 6:06:54 PM

Confirmations

5,386,376

Mined by

⛏️ P2SHAW3cHswaaT32mRKRsX8K2WP6ctr6c1kGQJ

Merkle Root

e522ee2e649457dfaf8b4f55e7f1a9ddf6ce06abe3a8a8265628aa3933c7de91

Transactions (4)

Coinbasee367030366f58e…326dfee8849069

1 in → 1 out9.0100 XPM109 B

AW3cHswa…r6c1kGQJ

f0c6e47355b45a…b289487faf2da3

106 in → 2 out867.2660 XPM15.40 KB

AGeVTwr6…pdLbQwHB Aba8Yb5s…ZPnX1T3K

d003c9f5440c65…842a12018a4a01

106 in → 2 out866.8385 XPM15.41 KB

AeTtJkMu…s2yov6cp AGeVTwr6…pdLbQwHB

aadbe72c7d2d86…59ae4513a44d66

1 in → 19 out73.9892 XPM805 B

AccQByBJ…G6HwiMao AQkrTz86…6aWuVYvM AURANnuU…acKggahH ATQ2RfSs…yao2HZMj AGnz4TTm…SQhppdqV

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.

3.730 × 10⁹⁵(96-digit number)

37301367136609620380…43198869635699425279

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

3.730 × 10⁹⁵(96-digit number)

37301367136609620380…43198869635699425279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.730 × 10⁹⁵(96-digit number)

37301367136609620380…43198869635699425281

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

7.460 × 10⁹⁵(96-digit number)

74602734273219240761…86397739271398850559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.460 × 10⁹⁵(96-digit number)

74602734273219240761…86397739271398850561

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

1.492 × 10⁹⁶(97-digit number)

14920546854643848152…72795478542797701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.492 × 10⁹⁶(97-digit number)

14920546854643848152…72795478542797701121

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

2.984 × 10⁹⁶(97-digit number)

29841093709287696304…45590957085595402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.984 × 10⁹⁶(97-digit number)

29841093709287696304…45590957085595402241

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

5.968 × 10⁹⁶(97-digit number)

59682187418575392608…91181914171190804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.968 × 10⁹⁶(97-digit number)

59682187418575392608…91181914171190804481

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 #1,453,406

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