Block #2,290,318

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/10/2017, 6:59:41 AM · Difficulty 10.9553 · 4,552,931 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8cebd1f8f7501ee000cb1f3c9d0e414e7ac80aba59bc7fbcc63b08875c7bc1b7

View on Chainz ↗

Height

#2,290,318

Difficulty

10.955284

Transactions

Size

1.00 KB

Version

Bits

0af48d7d

Nonce

939,124,782

Timestamp

9/10/2017, 6:59:41 AM

Confirmations

4,552,931

Mined by

⛏️ P2SHAbN3gRMk42e9BLkPXDviXqrvora1iMJime

Merkle Root

be425e6d88ac34355c85fbe1e8bf4f964a46718410e53a53676e2bbfd22a9962

Transactions (4)

Coinbasec8bd9f3835448c…48c2f12bb9a0cb

1 in → 1 out8.3500 XPM110 B

AbN3gRMk…a1iMJime

839ed5e2d5dcb4…df5a2730cbbb39

1 in → 2 out86085.4378 XPM225 B

AHFmFmdD…GjDPknVe AUV92CQL…PtRyBjSK

41e76ab8874e0b…a0844b486eab9e

1 in → 2 out5759.5479 XPM227 B

AWMLW3S9…j8CkFHgy AeQESrhU…2E4AuvSW

7bd5828fa8aae0…216349e3820e5a

2 in → 2 out518.9503 XPM374 B

AZgmLuNd…6T3k4SgB AQHVfK4N…Gsue8zPW

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.

8.505 × 10⁹⁴(95-digit number)

85057649608437998189…76796136199732954879

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

8.505 × 10⁹⁴(95-digit number)

85057649608437998189…76796136199732954879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.505 × 10⁹⁴(95-digit number)

85057649608437998189…76796136199732954881

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

1.701 × 10⁹⁵(96-digit number)

17011529921687599637…53592272399465909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.701 × 10⁹⁵(96-digit number)

17011529921687599637…53592272399465909761

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

3.402 × 10⁹⁵(96-digit number)

34023059843375199275…07184544798931819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.402 × 10⁹⁵(96-digit number)

34023059843375199275…07184544798931819521

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

6.804 × 10⁹⁵(96-digit number)

68046119686750398551…14369089597863639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.804 × 10⁹⁵(96-digit number)

68046119686750398551…14369089597863639041

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

1.360 × 10⁹⁶(97-digit number)

13609223937350079710…28738179195727278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.360 × 10⁹⁶(97-digit number)

13609223937350079710…28738179195727278081

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

2.721 × 10⁹⁶(97-digit number)

27218447874700159420…57476358391454556159

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 #2,290,318

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