Block #423,753

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/28/2014, 3:36:35 PM · Difficulty 10.3787 · 6,385,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd0415f8f69929a0f5e5f9bc994a5e4513d64f814a6b67e78f1a3b8f1885d1cc

View on Chainz ↗

Height

#423,753

Difficulty

10.378705

Transactions

Size

2.53 KB

Version

Bits

0a60f2d0

Nonce

180,056

Timestamp

2/28/2014, 3:36:35 PM

Confirmations

6,385,262

Mined by

⛏️ IwAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

0915920c2dc5e688898e123d797ef8e3ffd21d79753394e07789e12b942eab50

Transactions (4)

Coinbase25a1639ac6d337…d97b889471e939

1 in → 22 out9.3100 XPM811 B

AdFLJFhb…bsaVkAyh AZqjMFvv…G8aw2zC8 AcuM7XiJ…5uND8Jce AcgDwGo8…BBFwbjVo AQFhQpUS…HmKbSyAx

25e1d67568511b…e8d858008bb708

5 in → 15 out46.4000 XPM1.07 KB

AJMLR4ge…xorSP9K5 ALzeejWz…d7byrHth APc8LXDe…e1FgGz35 ANGAxNk6…Bb4uN2Ub AVy7vA87…WkzNt12Y

f4dc9e147921c7…d8398022a151a1

2 in → 2 out10.3706 XPM375 B

Ad1EDjhY…XMTpsi2c AWbTAdLC…8MPrZb4e

9a0c459d671d08…1a2f9643501d5d

1 in → 2 out5.1486 XPM225 B

AMNchnah…YvdtdypA AafXBxi8…MTbj7rvU

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.

6.365 × 10⁹⁷(98-digit number)

63657678976781378898…40997479373912671519

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

6.365 × 10⁹⁷(98-digit number)

63657678976781378898…40997479373912671519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.365 × 10⁹⁷(98-digit number)

63657678976781378898…40997479373912671521

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

1.273 × 10⁹⁸(99-digit number)

12731535795356275779…81994958747825343039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.273 × 10⁹⁸(99-digit number)

12731535795356275779…81994958747825343041

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

2.546 × 10⁹⁸(99-digit number)

25463071590712551559…63989917495650686079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.546 × 10⁹⁸(99-digit number)

25463071590712551559…63989917495650686081

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

5.092 × 10⁹⁸(99-digit number)

50926143181425103118…27979834991301372159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.092 × 10⁹⁸(99-digit number)

50926143181425103118…27979834991301372161

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

1.018 × 10⁹⁹(100-digit number)

10185228636285020623…55959669982602744319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.018 × 10⁹⁹(100-digit number)

10185228636285020623…55959669982602744321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.037 × 10⁹⁹(100-digit number)

20370457272570041247…11919339965205488639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #423,753

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