Block #2,127,737

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/22/2017, 5:15:10 AM · Difficulty 10.9180 · 4,711,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8683870b84bf6952930219d4df51341f5ae5ec392f06f1fae5c70a78d15961a1

View on Chainz ↗

Height

#2,127,737

Difficulty

10.917966

Transactions

Size

5.19 KB

Version

Bits

0aeaffca

Nonce

171,755,202

Timestamp

5/22/2017, 5:15:10 AM

Confirmations

4,711,058

Mined by

⛏️ P2SHASQhFpMPb2vRRYUWdZCFt22NPfVASucHNn

Merkle Root

5418354efdb7f4e5d41fce293f70263d2831dcbdc386b6d67411b758a53bc4b3

Transactions (2)

Coinbase99192cf9b0cd84…1800f06b249de7

1 in → 1 out8.4400 XPM110 B

ASQhFpMP…VASucHNn

74e182f8c0be53…b3655cb319940f

34 in → 2 out1200.0235 XPM5.00 KB

ATsGpLaK…6ivo8bfZ AL1pyz5t…QeunxaDV

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.

5.057 × 10⁹⁴(95-digit number)

50576809918642243721…25624387003481501599

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

5.057 × 10⁹⁴(95-digit number)

50576809918642243721…25624387003481501599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.057 × 10⁹⁴(95-digit number)

50576809918642243721…25624387003481501601

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

1.011 × 10⁹⁵(96-digit number)

10115361983728448744…51248774006963003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.011 × 10⁹⁵(96-digit number)

10115361983728448744…51248774006963003201

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

2.023 × 10⁹⁵(96-digit number)

20230723967456897488…02497548013926006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.023 × 10⁹⁵(96-digit number)

20230723967456897488…02497548013926006401

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

4.046 × 10⁹⁵(96-digit number)

40461447934913794977…04995096027852012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.046 × 10⁹⁵(96-digit number)

40461447934913794977…04995096027852012801

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

8.092 × 10⁹⁵(96-digit number)

80922895869827589954…09990192055704025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.092 × 10⁹⁵(96-digit number)

80922895869827589954…09990192055704025601

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

1.618 × 10⁹⁶(97-digit number)

16184579173965517990…19980384111408051199

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 #2,127,737

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