Block #434,757

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/8/2014, 11:27:21 AM · Difficulty 10.3515 · 6,390,795 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

377f9c9bfe436e46a94db4c80cc382367874c567b7025218d6629ca5e4a7fa05

View on Chainz ↗

Height

#434,757

Difficulty

10.351454

Transactions

Size

845 B

Version

Bits

0a59f8e8

Nonce

20,077

Timestamp

3/8/2014, 11:27:21 AM

Confirmations

6,390,795

Mined by

⛏️ P2SHAcnbkVvgFTwALeZA7q2NM2e47Gpn4CFXJj

Merkle Root

6f16af564a9af0d4f58e0d20230746f3e78cfaab247758b6114d4e2354899ead

Transactions (4)

Coinbased51a0f438ac5ea…29aa3635449711

1 in → 1 out9.3500 XPM109 B

AcnbkVvg…pn4CFXJj

e364f98a5390cd…95119339b98e18

1 in → 2 out10.5078 XPM226 B

AN1KJqah…faqCD6ke Ac9jVNaz…z2BHBX6Z

22041a286f6b4e…78843c0de71e4d

1 in → 1 out2.9905 XPM192 B

ATN6eQLm…hMs7kfrJ

ead9fc32e7b070…3ec2ad593ce3b4

1 in → 2 out6.6390 XPM225 B

AK5eMZv7…7wDmjJxU AKuvM2Vv…E7VmsCkz

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.

2.172 × 10¹⁰²(103-digit number)

21725680458155690095…26683996079586805599

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

2.172 × 10¹⁰²(103-digit number)

21725680458155690095…26683996079586805599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.172 × 10¹⁰²(103-digit number)

21725680458155690095…26683996079586805601

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

4.345 × 10¹⁰²(103-digit number)

43451360916311380191…53367992159173611199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.345 × 10¹⁰²(103-digit number)

43451360916311380191…53367992159173611201

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

8.690 × 10¹⁰²(103-digit number)

86902721832622760382…06735984318347222399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.690 × 10¹⁰²(103-digit number)

86902721832622760382…06735984318347222401

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

1.738 × 10¹⁰³(104-digit number)

17380544366524552076…13471968636694444799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.738 × 10¹⁰³(104-digit number)

17380544366524552076…13471968636694444801

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

3.476 × 10¹⁰³(104-digit number)

34761088733049104152…26943937273388889599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.476 × 10¹⁰³(104-digit number)

34761088733049104152…26943937273388889601

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 #434,757

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