Block #3,451,208

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/27/2019, 12:02:51 PM · Difficulty 10.9794 · 3,389,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9df07d6a1c4b5162e3cc75b6c246d088e4ed6febcb25b7c82cd85d09a572b2c8

View on Chainz ↗

Height

#3,451,208

Difficulty

10.979397

Transactions

Size

3.45 KB

Version

Bits

0afab9c5

Nonce

1,610,347,275

Timestamp

11/27/2019, 12:02:51 PM

Confirmations

3,389,994

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMz Visit pool ↗

Merkle Root

965dd45fc5126bfa7ff04736d4c44dcb7caf781f053bc96757d5f86e7eb360b2

Transactions (3)

Coinbasea4b4ef1e22afff…08f2ce73c8b36a

1 in → 1 out8.3300 XPM109 B

AXfJqzUb…HXeXmjMz

0b4357aa2e5cb9…2ebc2b269c87ac

1 in → 2 out8.2700 XPM191 B

AQSubPmX…k13gFnPE ASiq2qtK…VMhmk7yL

b9bb74ab2eec35…281d53f2ffd6b7

21 in → 1 out210.7221 XPM3.07 KB

AXoSyMCe…Z8KXiWkn

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.

5.583 × 10⁹⁴(95-digit number)

55838550499357031040…11382435533671485759

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

5.583 × 10⁹⁴(95-digit number)

55838550499357031040…11382435533671485759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.583 × 10⁹⁴(95-digit number)

55838550499357031040…11382435533671485761

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

1.116 × 10⁹⁵(96-digit number)

11167710099871406208…22764871067342971519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.116 × 10⁹⁵(96-digit number)

11167710099871406208…22764871067342971521

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

2.233 × 10⁹⁵(96-digit number)

22335420199742812416…45529742134685943039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.233 × 10⁹⁵(96-digit number)

22335420199742812416…45529742134685943041

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

4.467 × 10⁹⁵(96-digit number)

44670840399485624832…91059484269371886079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.467 × 10⁹⁵(96-digit number)

44670840399485624832…91059484269371886081

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

8.934 × 10⁹⁵(96-digit number)

89341680798971249665…82118968538743772159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.934 × 10⁹⁵(96-digit number)

89341680798971249665…82118968538743772161

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

1.786 × 10⁹⁶(97-digit number)

17868336159794249933…64237937077487544319

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 #3,451,208

Cookie Preferences