Block #2,139,006

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/31/2017, 9:15:53 AM · Difficulty 10.8802 · 4,703,251 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e8a4adba9dbfdf04de87e436fe8829101f3a6bf50dd914493c0f0a53fa0ab6f

View on Chainz ↗

Height

#2,139,006

Difficulty

10.880179

Transactions

Size

1.14 KB

Version

Bits

0ae15362

Nonce

1,459,112,159

Timestamp

5/31/2017, 9:15:53 AM

Confirmations

4,703,251

Mined by

⛏️ P2SHAGaD3dEfLuYJKscwuAQyoPXYUBhwtXzoTB

Merkle Root

867a4d4f9eec774bbddbd15db373bd8b15724c8f1a282a2e19cc32d31718bb3c

Transactions (2)

Coinbaseaf5bf458d09390…5229547f40e5e6

1 in → 1 out8.4500 XPM109 B

AGaD3dEf…hwtXzoTB

2a0e3c6b35637e…e8663ff293e8f7

6 in → 2 out957.3725 XPM964 B

Ae7ZEPhx…BXC8MGSx ARjf7CQe…KGgXHaQV

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.

2.774 × 10⁹⁴(95-digit number)

27743121636237163415…20061510865916342839

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

2.774 × 10⁹⁴(95-digit number)

27743121636237163415…20061510865916342839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.774 × 10⁹⁴(95-digit number)

27743121636237163415…20061510865916342841

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

5.548 × 10⁹⁴(95-digit number)

55486243272474326830…40123021731832685679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.548 × 10⁹⁴(95-digit number)

55486243272474326830…40123021731832685681

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

1.109 × 10⁹⁵(96-digit number)

11097248654494865366…80246043463665371359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.109 × 10⁹⁵(96-digit number)

11097248654494865366…80246043463665371361

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

2.219 × 10⁹⁵(96-digit number)

22194497308989730732…60492086927330742719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.219 × 10⁹⁵(96-digit number)

22194497308989730732…60492086927330742721

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

4.438 × 10⁹⁵(96-digit number)

44388994617979461464…20984173854661485439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.438 × 10⁹⁵(96-digit number)

44388994617979461464…20984173854661485441

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

8.877 × 10⁹⁵(96-digit number)

88777989235958922928…41968347709322970879

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 #2,139,006

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