Block #250,466

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 12:35:58 PM · Difficulty 9.9684 · 6,545,076 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2df5bb74605b6e6e6c42c5ef8379ff62d782c707e4747f02db42a60b3d4d96a9

View on Chainz ↗

Height

#250,466

Difficulty

9.968376

Transactions

Size

1.22 KB

Version

Bits

09f7e777

Nonce

61,117

Timestamp

11/8/2013, 12:35:58 PM

Confirmations

6,545,076

Mined by

⛏️ P2SHAefNmfCCiMUgcSMoZqwmWZgc6ARj9JS3UM

Merkle Root

977a7f60c47f432bd20992908b2e445e4ad7ad2f6b9ecaa5982339b7ab7e3807

Transactions (5)

Coinbased0b74d52ce4e4d…2bf647284feb99

1 in → 1 out10.0900 XPM109 B

AefNmfCC…Rj9JS3UM

ccb98725537f7f…54cbe2b5189e0a

1 in → 2 out248.9900 XPM227 B

AGA7RwEw…viJ843aA AZd9MT9j…5jj5HB1f

d5c9830c4eaa88…8e5f30f1c2d4f1

2 in → 2 out20.1100 XPM375 B

AcnKNMPr…jk6j4UeY Ab1hhPzi…URi5woLf

22dd2435f18510…62ec08f36d08fd

1 in → 2 out10.0500 XPM226 B

AKEAYrgp…BHg61Y99 AU7zZewt…PHtR5tZd

355b4c81558ec9…84c27994078354

1 in → 2 out4.6862 XPM225 B

AaVFHFSq…bCnX1Bpw AM8W9jLg…w7bb9Bms

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.

1.434 × 10⁹⁵(96-digit number)

14342949008916631885…34314341230453232639

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

1.434 × 10⁹⁵(96-digit number)

14342949008916631885…34314341230453232639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.434 × 10⁹⁵(96-digit number)

14342949008916631885…34314341230453232641

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

2.868 × 10⁹⁵(96-digit number)

28685898017833263770…68628682460906465279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.868 × 10⁹⁵(96-digit number)

28685898017833263770…68628682460906465281

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

5.737 × 10⁹⁵(96-digit number)

57371796035666527541…37257364921812930559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.737 × 10⁹⁵(96-digit number)

57371796035666527541…37257364921812930561

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

1.147 × 10⁹⁶(97-digit number)

11474359207133305508…74514729843625861119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.147 × 10⁹⁶(97-digit number)

11474359207133305508…74514729843625861121

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

2.294 × 10⁹⁶(97-digit number)

22948718414266611016…49029459687251722239

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