Block #3,101,250

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/20/2019, 2:33:56 AM · Difficulty 11.1433 · 3,740,255 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

777eb3e4c8453b1ad1015e00d7d78c136874854b81435c1008856c204249d919

View on Chainz ↗

Height

#3,101,250

Difficulty

11.143299

Transactions

Size

2.39 KB

Version

Bits

0b24af40

Nonce

2,084,272,849

Timestamp

3/20/2019, 2:33:56 AM

Confirmations

3,740,255

Mined by

⛏️ nAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

8fa243377522bde8a2dea8dc1f1afaa8148701b462baafe178a543982ebce14e

Transactions (5)

Coinbasecdb2aa0e67ae0f…c6db28894a9b91

1 in → 1 out8.0900 XPM109 B

AbXwmGxD…4XXYP765

0cef2fbbb8565f…9a3dbdf7258767

1 in → 2 out199.5609 XPM227 B

AbXwmGxD…4XXYP765 AU9aRTp8…Do4wGwGa

62dc53a560f16b…af44cca78ef9c6

10 in → 2 out50.0328 XPM1.39 KB

AbXwmGxD…4XXYP765 ARx5pvS5…qXT1H2zv

0dcb8ed73ad8b6…457eccca0205e4

2 in → 2 out10.1403 XPM374 B

AevxZoN3…fwTLU9Fn AbXwmGxD…4XXYP765

998cb2cd0d999c…67d753c9388728

1 in → 2 out2.1006 XPM227 B

AbXwmGxD…4XXYP765 AJzfvyP2…3cFWGp8A

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.

2.405 × 10⁹⁵(96-digit number)

24051359242319797698…73547002180891244799

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

2.405 × 10⁹⁵(96-digit number)

24051359242319797698…73547002180891244799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.405 × 10⁹⁵(96-digit number)

24051359242319797698…73547002180891244801

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

4.810 × 10⁹⁵(96-digit number)

48102718484639595396…47094004361782489599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.810 × 10⁹⁵(96-digit number)

48102718484639595396…47094004361782489601

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

9.620 × 10⁹⁵(96-digit number)

96205436969279190792…94188008723564979199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.620 × 10⁹⁵(96-digit number)

96205436969279190792…94188008723564979201

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

1.924 × 10⁹⁶(97-digit number)

19241087393855838158…88376017447129958399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.924 × 10⁹⁶(97-digit number)

19241087393855838158…88376017447129958401

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

3.848 × 10⁹⁶(97-digit number)

38482174787711676317…76752034894259916799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.848 × 10⁹⁶(97-digit number)

38482174787711676317…76752034894259916801

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

7.696 × 10⁹⁶(97-digit number)

76964349575423352634…53504069788519833599

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 #3,101,250

Cookie Preferences