Block #4,606,689

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/14/2022, 8:45:45 PM · Difficulty 10.8544 · 2,224,498 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9c6c2b08d9f8279f4c03b978c3076675bdaa498e90c3fb712703376f8206d3f

View on Chainz ↗

Height

#4,606,689

Difficulty

10.854401

Transactions

Size

10.21 KB

Version

Bits

0adaba03

Nonce

770,814,390

Timestamp

2/14/2022, 8:45:45 PM

Confirmations

2,224,498

Mined by

⛏️ P2SHAZ6QziuQaHDZkwWr125jSJcs23s7PjgzRb

Merkle Root

c07507e8b55060f20d8d68626d1af151016f01250a72255a0fc3a2d3a1569ff9

Transactions (3)

Coinbase0432a2eb6a1f2e…a3eb6ce0f318cf

1 in → 1 out8.5800 XPM110 B

AZ6QziuQ…s7PjgzRb

4170ee5441d8d1…01616acd7f8b52

76 in → 2 out638.9717 XPM8.57 KB

ATK5FqFY…btyiovww AZ6QziuQ…s7PjgzRb

30b92e6a64bb7b…ce3ec6a5d51b7d

12 in → 2 out100.3123 XPM1.44 KB

AZ6QziuQ…s7PjgzRb ARezZb4y…FxP7ivbi

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.

8.174 × 10⁹⁴(95-digit number)

81745117637847972696…16577829414884070399

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

8.174 × 10⁹⁴(95-digit number)

81745117637847972696…16577829414884070399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.174 × 10⁹⁴(95-digit number)

81745117637847972696…16577829414884070401

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

1.634 × 10⁹⁵(96-digit number)

16349023527569594539…33155658829768140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.634 × 10⁹⁵(96-digit number)

16349023527569594539…33155658829768140801

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

3.269 × 10⁹⁵(96-digit number)

32698047055139189078…66311317659536281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.269 × 10⁹⁵(96-digit number)

32698047055139189078…66311317659536281601

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

6.539 × 10⁹⁵(96-digit number)

65396094110278378157…32622635319072563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.539 × 10⁹⁵(96-digit number)

65396094110278378157…32622635319072563201

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

1.307 × 10⁹⁶(97-digit number)

13079218822055675631…65245270638145126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.307 × 10⁹⁶(97-digit number)

13079218822055675631…65245270638145126401

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

2.615 × 10⁹⁶(97-digit number)

26158437644111351262…30490541276290252799

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 #4,606,689

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