Block #3,086,965

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/10/2019, 2:02:51 PM · Difficulty 11.0391 · 3,755,014 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec6c91aacc7dee0b7f1c1f0cb7e6329a929bfffaf4e249095aaec4eeaea2b5b8

View on Chainz ↗

Height

#3,086,965

Difficulty

11.039095

Transactions

Size

1.19 KB

Version

Bits

0b0a0229

Nonce

776,642,080

Timestamp

3/10/2019, 2:02:51 PM

Confirmations

3,755,014

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

7439d5928a9f1666fed04d1d0e9b6b4f4914830429d6747bbec17db70d513bf8

Transactions (4)

Coinbasef50ee87c1612b5…ab20fd0ff0efd8

1 in → 1 out8.2200 XPM110 B

AbXwmGxD…4XXYP765

37bc162974d666…a05e0ba743a48b

2 in → 2 out16.4100 XPM306 B

ANiRSGwW…LtXULkMk AWRWZJhB…d4YmN6SJ

51542c5b245737…f8c9e72b4b2739

2 in → 2 out14.6100 XPM341 B

AVyDjMkm…1ji94eQY APGUc3dJ…2uKsdSWR

ec3b68e3743df9…ac2f6fefe4acd3

2 in → 2 out11.0100 XPM374 B

APhW6dpZ…KiJek1sw Ac1AoN5f…Wn5GBSZA

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.

7.997 × 10⁹⁴(95-digit number)

79978373915047957953…10134490594808375359

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

7.997 × 10⁹⁴(95-digit number)

79978373915047957953…10134490594808375359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.997 × 10⁹⁴(95-digit number)

79978373915047957953…10134490594808375361

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

1.599 × 10⁹⁵(96-digit number)

15995674783009591590…20268981189616750719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.599 × 10⁹⁵(96-digit number)

15995674783009591590…20268981189616750721

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

3.199 × 10⁹⁵(96-digit number)

31991349566019183181…40537962379233501439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.199 × 10⁹⁵(96-digit number)

31991349566019183181…40537962379233501441

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

6.398 × 10⁹⁵(96-digit number)

63982699132038366362…81075924758467002879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.398 × 10⁹⁵(96-digit number)

63982699132038366362…81075924758467002881

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

1.279 × 10⁹⁶(97-digit number)

12796539826407673272…62151849516934005759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.279 × 10⁹⁶(97-digit number)

12796539826407673272…62151849516934005761

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

2.559 × 10⁹⁶(97-digit number)

25593079652815346545…24303699033868011519

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 #3,086,965

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