XPMPrime Explorer

Synced#6,836,990

Block #3,506,049

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/9/2020, 1:36:06 AM · Difficulty 10.9303 · 3,330,942 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b15232eefa7773376c00304f179b37b9dc96489a160902c6002e5ecd1bae2842

View on Chainz ↗

Height

#3,506,049

Difficulty

10.930308

Transactions

8

Size

51.07 KB

Version

2

Bits

0aee28a6

Nonce

1,398,533,907

Timestamp

1/9/2020, 1:36:06 AM

Confirmations

3,330,942

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

2440cc5a2e6e7805f5eae405b4417334577cd6cc9449a0738fc65c4113154a7e

Transactions (8)

Coinbasee1e409b7eb0606…dbbb3893f971f4

1 in → 1 out8.9200 XPM110 B

ASiq2qtK…VMhmk7yL

e211d86159d335…422128ab2b0775

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

fa3d722acd0cd6…a627b94bfa7c26

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

e46217e01c2203…e91adbb63351d4

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

f1ec42a88e504d…325bacb7eefce0

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

79b057e4bfc5e7…2e3c9196697aa3

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

d77abd561777e8…bf348e8f7876f2

50 in → 1 out6665.2803 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

3405cf03548ed5…2220b911678700

50 in → 1 out199.9200 XPM7.27 KB

ALcTQaSP…1C5Yf2Zi

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.

1.228 × 10⁹⁵(96-digit number)

12285650141115243797…58137523429306507199

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

1.228 × 10⁹⁵(96-digit number)

12285650141115243797…58137523429306507199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.228 × 10⁹⁵(96-digit number)

12285650141115243797…58137523429306507201

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

2.457 × 10⁹⁵(96-digit number)

24571300282230487595…16275046858613014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.457 × 10⁹⁵(96-digit number)

24571300282230487595…16275046858613014401

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

4.914 × 10⁹⁵(96-digit number)

49142600564460975191…32550093717226028799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.914 × 10⁹⁵(96-digit number)

49142600564460975191…32550093717226028801

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

9.828 × 10⁹⁵(96-digit number)

98285201128921950383…65100187434452057599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.828 × 10⁹⁵(96-digit number)

98285201128921950383…65100187434452057601

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

1.965 × 10⁹⁶(97-digit number)

19657040225784390076…30200374868904115199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.965 × 10⁹⁶(97-digit number)

19657040225784390076…30200374868904115201

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

3.931 × 10⁹⁶(97-digit number)

39314080451568780153…60400749737808230399

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

Circulating Supply:57,940,229 XPM·at block #6,836,990 · updates every 60s

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