Block #1,476,219

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/28/2016, 11:04:41 PM · Difficulty 10.6981 · 5,368,578 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

54720dc0914af72df1c7fd460bcfc25bb3adeb2e563b499cb5a23a33d13df1d7

View on Chainz ↗

Height

#1,476,219

Difficulty

10.698073

Transactions

Size

1.01 KB

Version

Bits

0ab2b4ea

Nonce

691,712,269

Timestamp

2/28/2016, 11:04:41 PM

Confirmations

5,368,578

Mined by

⛏️ P2SHAKKAR1Vp11MeEgSoKqEmu3bAd25H38gxzM

Merkle Root

9c813bd0201d6eb41abfae625b0d39e5e647a1bc7de663c7dd7e4679ee350439

Transactions (2)

Coinbased0789b97122672…f7d2c0aff0c6be

1 in → 1 out8.7300 XPM109 B

AKKAR1Vp…5H38gxzM

73b0095f0654ab…cca5eb1f92ece4

1 in → 20 out232.8732 XPM837 B

AQ58PbTK…dAvjNiT6 AcFmN2WM…akTDYhkE AbKTBQJ5…TsaoMvRw AXd9ZNpX…741Nk3EK AZ2Dv6vs…YoKVyFme

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.

2.274 × 10⁹⁴(95-digit number)

22746233056631001904…33121116447508094679

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

2.274 × 10⁹⁴(95-digit number)

22746233056631001904…33121116447508094679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.274 × 10⁹⁴(95-digit number)

22746233056631001904…33121116447508094681

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

4.549 × 10⁹⁴(95-digit number)

45492466113262003808…66242232895016189359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.549 × 10⁹⁴(95-digit number)

45492466113262003808…66242232895016189361

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

9.098 × 10⁹⁴(95-digit number)

90984932226524007617…32484465790032378719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.098 × 10⁹⁴(95-digit number)

90984932226524007617…32484465790032378721

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

1.819 × 10⁹⁵(96-digit number)

18196986445304801523…64968931580064757439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.819 × 10⁹⁵(96-digit number)

18196986445304801523…64968931580064757441

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

3.639 × 10⁹⁵(96-digit number)

36393972890609603046…29937863160129514879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.639 × 10⁹⁵(96-digit number)

36393972890609603046…29937863160129514881

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

7.278 × 10⁹⁵(96-digit number)

72787945781219206093…59875726320259029759

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 #1,476,219

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