Block #255,298

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 4:51:54 AM · Difficulty 9.9741 · 6,539,751 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

34a4e1c86d5af314f72286f8c8f775f9769989cb7a3d2a743ff3ecfc042c966c

View on Chainz ↗

Height

#255,298

Difficulty

9.974087

Transactions

Size

1.21 KB

Version

Bits

09f95dcc

Nonce

3,346

Timestamp

11/11/2013, 4:51:54 AM

Confirmations

6,539,751

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

c3634a1733b106d03450ba7a44cdddb5e5a09bc3327c737f38e09acfa4a1a847

Transactions (5)

Coinbased64c61fe1a973a…584c5014d33ae0

1 in → 2 out10.0806 XPM137 B

AZDUEbdS…RYKMRZET Abiw8n3q…ZnZfgvQW

60dbbb11a7d198…3310d2f6753ad4

1 in → 1 out2.9900 XPM192 B

AZLL3Fjt…ez6JMifD

498febd42611b7…5acf67fa4f9711

1 in → 2 out8.0199 XPM227 B

AXCCsfyG…SSSFr1ZK AMyCTjtU…HKqAncnm

9790613697b54b…f4f68231f53967

1 in → 2 out3.9920 XPM225 B

AeQs3357…pHaUXQ7A ASnSjgQg…fewAaNPL

a51555cf6ce438…915d69eedbe0b6

1 in → 6 out9.4522 XPM362 B

AG9SfhhW…sSJdWcrQ AVHcc9zb…JkngbvXL AVg5YGji…Aq7MMxRC AMignMR8…u4Se3849 ASTnAjxL…Avpty1Md

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.

8.259 × 10⁹⁵(96-digit number)

82599610463471744191…77102824202559071999

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

8.259 × 10⁹⁵(96-digit number)

82599610463471744191…77102824202559071999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.259 × 10⁹⁵(96-digit number)

82599610463471744191…77102824202559072001

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

1.651 × 10⁹⁶(97-digit number)

16519922092694348838…54205648405118143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.651 × 10⁹⁶(97-digit number)

16519922092694348838…54205648405118144001

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

3.303 × 10⁹⁶(97-digit number)

33039844185388697676…08411296810236287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.303 × 10⁹⁶(97-digit number)

33039844185388697676…08411296810236288001

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

6.607 × 10⁹⁶(97-digit number)

66079688370777395353…16822593620472575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.607 × 10⁹⁶(97-digit number)

66079688370777395353…16822593620472576001

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

1.321 × 10⁹⁷(98-digit number)

13215937674155479070…33645187240945151999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.321 × 10⁹⁷(98-digit number)

13215937674155479070…33645187240945152001

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