Block #3,064,196

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/22/2019, 4:54:51 PM · Difficulty 10.9961 · 3,777,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe603503d126245e4f935dfab335623ba7ec8af2f6d8f80be6ceceeef1765b1e

View on Chainz ↗

Height

#3,064,196

Difficulty

10.996083

Transactions

Size

2.57 KB

Version

Bits

0afeff51

Nonce

72,683,683

Timestamp

2/22/2019, 4:54:51 PM

Confirmations

3,777,224

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

9123172f74a159a893c215541420cabe873ddefbcbba51fb44c64003af201eef

Transactions (5)

Coinbase10e840e2ad3479…37c917d328d84a

1 in → 1 out8.3100 XPM110 B

AbXwmGxD…4XXYP765

a035f56426f4f5…598202b6a2af09

10 in → 2 out1901.0783 XPM1.52 KB

APqqEHjX…y4mtBfer ANeo8URS…WrC2zfLb

4cf9460a772062…bfa284d13f8acf

1 in → 2 out8.2200 XPM193 B

ALxskxzJ…mwRWwWjn AbXwmGxD…4XXYP765

f059975fc4e04b…d880936dfe193d

2 in → 2 out11.4284 XPM341 B

AbXwmGxD…4XXYP765 AevxZoN3…fwTLU9Fn

de38554db95dc2…de363a331a9f2b

2 in → 2 out11.3672 XPM340 B

AbXwmGxD…4XXYP765 AK7gTG1e…nDmgCzsN

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.

1.202 × 10⁹⁴(95-digit number)

12021182493150482539…60779705264826035999

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

1.202 × 10⁹⁴(95-digit number)

12021182493150482539…60779705264826035999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.202 × 10⁹⁴(95-digit number)

12021182493150482539…60779705264826036001

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

2.404 × 10⁹⁴(95-digit number)

24042364986300965079…21559410529652071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.404 × 10⁹⁴(95-digit number)

24042364986300965079…21559410529652072001

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

4.808 × 10⁹⁴(95-digit number)

48084729972601930159…43118821059304143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.808 × 10⁹⁴(95-digit number)

48084729972601930159…43118821059304144001

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

9.616 × 10⁹⁴(95-digit number)

96169459945203860319…86237642118608287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.616 × 10⁹⁴(95-digit number)

96169459945203860319…86237642118608288001

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

1.923 × 10⁹⁵(96-digit number)

19233891989040772063…72475284237216575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.923 × 10⁹⁵(96-digit number)

19233891989040772063…72475284237216576001

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

3.846 × 10⁹⁵(96-digit number)

38467783978081544127…44950568474433151999

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 #3,064,196

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