Block #2,129,174

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/23/2017, 12:12:24 PM · Difficulty 10.9109 · 4,715,245 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8bf1288276dc76cf05e0843b9e485165cbc4be9bd5e25520a9cefea016758597

View on Chainz ↗

Height

#2,129,174

Difficulty

10.910893

Transactions

Size

1.48 KB

Version

Bits

0ae93042

Nonce

975,115,653

Timestamp

5/23/2017, 12:12:24 PM

Confirmations

4,715,245

Mined by

⛏️ P2SHAPJCrz7RMfkkVdhVCG5mcfTaMvGWZJE9oN

Merkle Root

7199cfde41ab62ce09384fe2439f365c4571f7059758d895a10a7a734d3557c1

Transactions (5)

Coinbase3a1e05c540676a…4774bbdba0712c

1 in → 1 out8.4300 XPM109 B

APJCrz7R…GWZJE9oN

69f6d745cd155a…bf73e447db96ff

3 in → 2 out1248.9800 XPM521 B

AMTtv8JB…RjAMqUFh ASyyuKCA…WrdFb3ZE

20210469ae2494…667743576509cc

1 in → 2 out1236.5049 XPM225 B

AY3Qn6ca…4BFz1GBb AXo7xgdi…w5m2AWXo

28939960e92ff3…c2b39eb44365b9

2 in → 2 out11.7091 XPM341 B

AbxbAUaL…uX3gA9SK AKRSVEYd…wz7YE2Rm

db55d81132ee01…f5baaf1a53074f

1 in → 2 out3.9900 XPM227 B

AZfrnjXa…iW3cj5BL AckWWKV2…CnnJ6rNF

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.

4.096 × 10⁹⁴(95-digit number)

40969063090571161998…13979520695360716799

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

4.096 × 10⁹⁴(95-digit number)

40969063090571161998…13979520695360716799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.096 × 10⁹⁴(95-digit number)

40969063090571161998…13979520695360716801

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

8.193 × 10⁹⁴(95-digit number)

81938126181142323996…27959041390721433599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.193 × 10⁹⁴(95-digit number)

81938126181142323996…27959041390721433601

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

1.638 × 10⁹⁵(96-digit number)

16387625236228464799…55918082781442867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.638 × 10⁹⁵(96-digit number)

16387625236228464799…55918082781442867201

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

3.277 × 10⁹⁵(96-digit number)

32775250472456929598…11836165562885734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.277 × 10⁹⁵(96-digit number)

32775250472456929598…11836165562885734401

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

6.555 × 10⁹⁵(96-digit number)

65550500944913859197…23672331125771468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.555 × 10⁹⁵(96-digit number)

65550500944913859197…23672331125771468801

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

1.311 × 10⁹⁶(97-digit number)

13110100188982771839…47344662251542937599

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 #2,129,174

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