Block #3,667,630

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2020, 6:28:46 AM · Difficulty 10.8840 · 3,141,949 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81b98c41e8b260713d05cf66a121536daf31663bb5ad2b87a67bbb25485c537c

View on Chainz ↗

Height

#3,667,630

Difficulty

10.883974

Transactions

Size

1.97 KB

Version

Bits

0ae24c19

Nonce

290,356,974

Timestamp

5/2/2020, 6:28:46 AM

Confirmations

3,141,949

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

34dd72961b779deb2ddc065f08829cf417bba6784cd7d6da16ee84e45f8f9582

Transactions (5)

Coinbased65173e042a851…8a0d4750cca484

1 in → 1 out8.4800 XPM110 B

ASiq2qtK…VMhmk7yL

04f3f904a7a375…9131210e9235cf

4 in → 2 out33.7200 XPM534 B

AMDJ5Dpx…2KovYaKo ASiq2qtK…VMhmk7yL

387aa7c8868443…55b138e6189c04

1 in → 2 out8.4200 XPM192 B

ANn2Zx9p…WKMq9Pta ASiq2qtK…VMhmk7yL

38d6759d42ff97…a58fd51d269767

3 in → 2 out23.7142 XPM456 B

ASgJoPyT…Nqx4EoES ASiq2qtK…VMhmk7yL

d5d809bf5f6dc4…52a12f03d305e6

4 in → 2 out10.1628 XPM637 B

ASiq2qtK…VMhmk7yL AWxHVeWs…Q7RMs542

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.

2.521 × 10⁹⁷(98-digit number)

25217790065606147744…79927532359738716159

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

2.521 × 10⁹⁷(98-digit number)

25217790065606147744…79927532359738716159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.521 × 10⁹⁷(98-digit number)

25217790065606147744…79927532359738716161

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

5.043 × 10⁹⁷(98-digit number)

50435580131212295489…59855064719477432319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.043 × 10⁹⁷(98-digit number)

50435580131212295489…59855064719477432321

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

1.008 × 10⁹⁸(99-digit number)

10087116026242459097…19710129438954864639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.008 × 10⁹⁸(99-digit number)

10087116026242459097…19710129438954864641

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

2.017 × 10⁹⁸(99-digit number)

20174232052484918195…39420258877909729279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.017 × 10⁹⁸(99-digit number)

20174232052484918195…39420258877909729281

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

4.034 × 10⁹⁸(99-digit number)

40348464104969836391…78840517755819458559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.034 × 10⁹⁸(99-digit number)

40348464104969836391…78840517755819458561

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

Block #3,667,630

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