Block #3,550,109

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/8/2020, 5:21:21 PM · Difficulty 10.9306 · 3,267,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09333a644e2fdcfb207048455e502464378718d7b145880bcba445490183e4d1

View on Chainz ↗

Height

#3,550,109

Difficulty

10.930573

Transactions

Size

845 B

Version

Bits

0aee3a06

Nonce

1,167,889,657

Timestamp

2/8/2020, 5:21:21 PM

Confirmations

3,267,137

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

c2c4837ee7b7dad8966e5086d57673059e12f5e5e977b324e64c9833bcbcb643

Transactions (4)

Coinbase6a1d006e1c9733…1ec416d4f0a841

1 in → 1 out8.3900 XPM109 B

ASiq2qtK…VMhmk7yL

b5ed1194de5a05…728361ef65a549

1 in → 2 out8.3400 XPM192 B

AXfJqzUb…HXeXmjMz ARL5pRbV…GErcKqqq

da4c7d7a3fd8a0…8d9ea7cd0e72be

1 in → 2 out4.3300 XPM226 B

AJMxYZjf…M1jTTdNb AXfJqzUb…HXeXmjMz

6ae8c92c4f6633…6dd7d38879ce45

1 in → 2 out4.3300 XPM227 B

ANPMMEMP…865wkbqX AXfJqzUb…HXeXmjMz

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.

2.253 × 10⁹⁷(98-digit number)

22535753130977202350…75922321267819806719

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

2.253 × 10⁹⁷(98-digit number)

22535753130977202350…75922321267819806719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.253 × 10⁹⁷(98-digit number)

22535753130977202350…75922321267819806721

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

4.507 × 10⁹⁷(98-digit number)

45071506261954404701…51844642535639613439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.507 × 10⁹⁷(98-digit number)

45071506261954404701…51844642535639613441

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

9.014 × 10⁹⁷(98-digit number)

90143012523908809402…03689285071279226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.014 × 10⁹⁷(98-digit number)

90143012523908809402…03689285071279226881

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

1.802 × 10⁹⁸(99-digit number)

18028602504781761880…07378570142558453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.802 × 10⁹⁸(99-digit number)

18028602504781761880…07378570142558453761

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

3.605 × 10⁹⁸(99-digit number)

36057205009563523760…14757140285116907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.605 × 10⁹⁸(99-digit number)

36057205009563523760…14757140285116907521

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

7.211 × 10⁹⁸(99-digit number)

72114410019127047521…29514280570233815039

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 #3,550,109

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