Block #1,073,835

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2015, 3:41:12 PM · Difficulty 10.7417 · 5,733,962 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4c30cd10b544ef01dd8401faea3d521e79e940ba05506d4b565720314d014fc

View on Chainz ↗

Height

#1,073,835

Difficulty

10.741692

Transactions

Size

13.58 KB

Version

Bits

0abddf84

Nonce

214,399,632

Timestamp

5/24/2015, 3:41:12 PM

Confirmations

5,733,962

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

192b080ccbe193c47c131ef026dd657fc32aef7edf019d5a1476929aa8d5a4be

Transactions (4)

Coinbase05666bdf676883…9c0c09ea7755d7

1 in → 1 out8.8000 XPM116 B

ANSXnLY2…Sd25TjkD

3794594d418db3…1252a34144f4eb

86 in → 2 out345.0000 XPM12.50 KB

ALoCYDrZ…4KRPh7hj AJda9EXJ…YUyCPsdc

17c49b1abdef5e…68f87b900952fb

2 in → 2 out12.2803 XPM372 B

ANNBoEaA…o6TzGWqw AL1hZgsg…iqLKdESt

26d486efc29c12…52077a51ebcc72

3 in → 2 out6.8811 XPM520 B

AX2bVAtJ…GpaxY2ja AHv9RfGp…UiuwkWcp

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.

5.473 × 10⁹⁶(97-digit number)

54731205883502647258…23693811320048249599

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

5.473 × 10⁹⁶(97-digit number)

54731205883502647258…23693811320048249599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.473 × 10⁹⁶(97-digit number)

54731205883502647258…23693811320048249601

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

1.094 × 10⁹⁷(98-digit number)

10946241176700529451…47387622640096499199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.094 × 10⁹⁷(98-digit number)

10946241176700529451…47387622640096499201

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

2.189 × 10⁹⁷(98-digit number)

21892482353401058903…94775245280192998399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.189 × 10⁹⁷(98-digit number)

21892482353401058903…94775245280192998401

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

4.378 × 10⁹⁷(98-digit number)

43784964706802117806…89550490560385996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.378 × 10⁹⁷(98-digit number)

43784964706802117806…89550490560385996801

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

8.756 × 10⁹⁷(98-digit number)

87569929413604235613…79100981120771993599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.756 × 10⁹⁷(98-digit number)

87569929413604235613…79100981120771993601

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 #1,073,835

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