Block #270,506

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 12:07:29 AM · Difficulty 9.9517 · 6,539,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d63d4328aa84232830cfd318f7b0fbb2ccee435bc34bc64e3782d64c5a74535

View on Chainz ↗

Height

#270,506

Difficulty

9.951720

Transactions

Size

15.00 KB

Version

Bits

09f3a3f3

Nonce

260,044

Timestamp

11/24/2013, 12:07:29 AM

Confirmations

6,539,286

Mined by

⛏️ P2SHAavTkidaAzoyaV2oN5F5r9uiNATsj4DYFE

Merkle Root

803da4437c2cfe9d96f3c24aee4495dbf1a3fb184e8312657327dd471e0d0491

Transactions (5)

Coinbasef01621deb7fdbb…f146217c02f811

1 in → 1 out10.2600 XPM109 B

AavTkida…Tsj4DYFE

aec36af8d9b528…b3c92bbabd02a5

7 in → 2 out68.0122 XPM909 B

AS812nwS…QX7hdxH6 AHQTgMeH…d5Fdrhmb

fb4b1e0d3274e1…ee53cdf4f641b4

1 in → 4 out10.0600 XPM260 B

AeKNrjNj…1NEq95Ta ASNYeTKF…CRfjh97X APEdUQu5…t45s5qQU AcADmAoe…8iNnoMzB

93a9eba8209353…b48d58ccd6e613

92 in → 1 out10.7649 XPM13.33 KB

ARyCdm88…sAKSwfEL

183716049be220…95dc2c87799ce6

2 in → 1 out1.9800 XPM340 B

AWKhcKD1…AK1RJ4a3

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.

5.776 × 10⁹⁰(91-digit number)

57766888170671273926…12343542359463657049

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

5.776 × 10⁹⁰(91-digit number)

57766888170671273926…12343542359463657049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.776 × 10⁹⁰(91-digit number)

57766888170671273926…12343542359463657051

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

1.155 × 10⁹¹(92-digit number)

11553377634134254785…24687084718927314099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.155 × 10⁹¹(92-digit number)

11553377634134254785…24687084718927314101

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

2.310 × 10⁹¹(92-digit number)

23106755268268509570…49374169437854628199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.310 × 10⁹¹(92-digit number)

23106755268268509570…49374169437854628201

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

4.621 × 10⁹¹(92-digit number)

46213510536537019141…98748338875709256399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.621 × 10⁹¹(92-digit number)

46213510536537019141…98748338875709256401

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

9.242 × 10⁹¹(92-digit number)

92427021073074038282…97496677751418512799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.242 × 10⁹¹(92-digit number)

92427021073074038282…97496677751418512801

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 #270,506

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