Block #411,624

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2014, 10:31:48 PM · Difficulty 10.4229 · 6,390,901 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77e5da470a512c6f6cef23e5c27cf564ab2b3844202214e48b4e7244c01f2cc2

View on Chainz ↗

Height

#411,624

Difficulty

10.422901

Transactions

Size

803 B

Version

Bits

0a6c433a

Nonce

184,918

Timestamp

2/19/2014, 10:31:48 PM

Confirmations

6,390,901

Mined by

⛏️ P2SHALVthvdBexuyeFHgma8YkVBnTzrNo2Y76q

Merkle Root

aa364dcf1e8eeb634a706f1acf3abf03a7bf98386b2b566e2e5621d88abfef2d

Transactions (3)

Coinbase0f523aadb49d84…900a52a54fe544

1 in → 1 out9.2100 XPM111 B

ALVthvdB…rNo2Y76q

c9bc3ede89090e…3e9f6ca78096bc

1 in → 2 out6.0690 XPM226 B

AWrC2JFy…kWYfqyXx AHBPTGaX…otvRZhWd

78f1f012e1dac3…ac48af189971ef

2 in → 2 out1.0155 XPM374 B

AJrASerw…ZzgTJ6FH Ac3adS2S…va6hWeMv

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.

2.659 × 10⁹⁸(99-digit number)

26597383767955918918…56619300743259821699

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

2.659 × 10⁹⁸(99-digit number)

26597383767955918918…56619300743259821699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.659 × 10⁹⁸(99-digit number)

26597383767955918918…56619300743259821701

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

5.319 × 10⁹⁸(99-digit number)

53194767535911837836…13238601486519643399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.319 × 10⁹⁸(99-digit number)

53194767535911837836…13238601486519643401

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

1.063 × 10⁹⁹(100-digit number)

10638953507182367567…26477202973039286799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.063 × 10⁹⁹(100-digit number)

10638953507182367567…26477202973039286801

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

2.127 × 10⁹⁹(100-digit number)

21277907014364735134…52954405946078573599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.127 × 10⁹⁹(100-digit number)

21277907014364735134…52954405946078573601

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

4.255 × 10⁹⁹(100-digit number)

42555814028729470269…05908811892157147199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.255 × 10⁹⁹(100-digit number)

42555814028729470269…05908811892157147201

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