Block #307,463

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 2:50:30 PM · Difficulty 9.9942 · 6,503,015 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09fe414cba24fd1d7ab69dc2c2de554dc1ef02a9314055e535dc0e397aef4126

View on Chainz ↗

Height

#307,463

Difficulty

9.994173

Transactions

Size

2.24 KB

Version

Bits

09fe8225

Nonce

51,722

Timestamp

12/12/2013, 2:50:30 PM

Confirmations

6,503,015

Mined by

⛏️ aRBAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

06bf1b61f2fc3e028669edfd01a26672dcd698b114d6aefbd1aa84d29254ed29

Transactions (4)

Coinbase26c26274d504d4…824ef85907ae87

1 in → 31 out9.9800 XPM1.09 KB

Aac9Hjdg…P4ktypc3 ASWX42VM…XypQABkY AMbCuLHZ…WSoStwkc AGHQBt42…kioRggo7 ALbnyRDo…sK52qx5d

aa950ad9f57b8b…65ba72436c9341

4 in → 1 out3.9900 XPM634 B

AGd1S7yh…xS25mQUS

44e3500a1f665c…242826a9aff712

1 in → 2 out5.4830 XPM227 B

AcQcu1QN…1Kfnq2ya ASiac4pd…1eM2V5nQ

fa522e75755ec2…ea9c6170c99760

1 in → 2 out5.4207 XPM225 B

AQTLhghT…dVtLthsA AGsZPR2M…TohGhvj8

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.

1.178 × 10⁹⁹(100-digit number)

11787441196905987216…00005778317245132799

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

1.178 × 10⁹⁹(100-digit number)

11787441196905987216…00005778317245132799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.178 × 10⁹⁹(100-digit number)

11787441196905987216…00005778317245132801

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

2.357 × 10⁹⁹(100-digit number)

23574882393811974433…00011556634490265599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.357 × 10⁹⁹(100-digit number)

23574882393811974433…00011556634490265601

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

4.714 × 10⁹⁹(100-digit number)

47149764787623948866…00023113268980531199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.714 × 10⁹⁹(100-digit number)

47149764787623948866…00023113268980531201

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

9.429 × 10⁹⁹(100-digit number)

94299529575247897732…00046226537961062399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.429 × 10⁹⁹(100-digit number)

94299529575247897732…00046226537961062401

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

1.885 × 10¹⁰⁰(101-digit number)

18859905915049579546…00092453075922124799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #307,463

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